See veebileht kasutab küpsiseid kasutaja sessiooni andmete hoidmiseks. Veebilehe kasutamisega nõustute ETISe kasutustingimustega. Loe rohkem
Olen nõus

Eugen Paal

https://www.etis.ee/CV/Paal_E/est

Teenistuskäik

Töökohad ja ametid
2005–...   
ASTRALGO R&D, Külalisteadur (0,50)
1998–2017   
Tallinn University of Technology, Professor of Mathematical Physics (1,00)
 
 
Haridustee
1986–1988   
Aspirantuur, elementaarosakeste töörühm, Eesti Teaduste Akadeemia Füüsika Instituut
1972–1977   
Teoreetiline ja matemaatiline füüsika, Füüsika-keemiateaduskond, Tartu Ülikool
 
 
Teadusorganisatsiooniline ja -administratiivne tegevus
2012−...   
Tallinna konverentsisaadik
2005−...   
ASTRALGO R&D; kolleegiumi liige
2004−...   
ISQS võrgustik, kolleegiumi liige
2002−...   
AGMP võrgustik, kaasasutaja, kolleegiumi liige, koordinaator
2014−2015   
Rahv. konv. Moduli - Operads - Dynamics (MOD) II, 03.-06. juuni 2014, Tallinn, korraldaja
2013−2014   
Rahv. konv. Moduli - Operads - Dynamics (MOD) I, 09.-11. juuli 2013, Kongsberg, Norra, kaaskorraldaja
2012−2014   
Rahv. konv. AGMP VIII, 09.-12. sept. 2012, Brno, Tšehhi Vabariik, kaaskorraldaja
2012−2014   
6. Euroopa matemaatikakongressi (ECM6) satelliitkonverents, 3Quantum: Algebra - Geometry - Information, 10.-13. juuli 2012, Tallinn, korraldaja
2012−2015   
Operaadid, deformatsioonid, dünaamika, ETF grant, grandihoidja
2012−2015   
Operaadid, deformatsioonid, dünaamika, Eesti Teadusfondi grant, grandihoidja
2011−2012   
AGMP & MP2 rahv. suvekool, Mathematical Topics in Quantum Mechanics and Quantum Information, 05.09. sept. 2011, Tjärnö, Rootsi, kaaskorraldaja
2011−2014   
Rahv. konv AGMP VII, 24.-26. okt. 2011, Mulhouse, Prantsusmaa, kaaskorraldaja
2010−2012   
Rahv. konv. AGMP VI, 25.-30. okt. 2010, Tjärnö, Rootsi, kaaskorraldaja
2009−2011   
Rahv. konv. AGMP V, 12.-16. okt. 2009, Banachi konverentsikeskus, Bedlewo, Poola, kaaskorraldaja
2009−2014   
J. Phys. Math., asutaja, peatoimetaja (2009-2014)
2008−2010   
Rahv. konv. AGMP IV, 09.-11. okt. 2008, Tartu, kaaskorraldaja
2007−2008   
Rahv. konv. AGMP III, 11.-13. okt. 2007, Göteborg, Rootsi, kaaskorraldaja
2007−2010   
Üldistatud Lie teooria, ETF grant, grandihoidja
2007−2010   
Üldistatud Lie teooria, Eesti Teadusfondi grant, grandihoidja
2006−2011   
Astralgo CC & Eugen Paal (FIE)
2006−2009   
Rahv. konv. AGMP II, 12.-14. okt. 2006, Lund, Rootsi, kaaskorraldaja
2006−2014   
J. Gen. Lie Theory Appl., asutaja, kirjastaja, peatoimetaja (2006-2014)
2005−2006   
Rahv. konv AGMP I, 8. okt. 2005, Tallinn, korraldaja
2003−2006   
Operaadid ja kohomoloogia, ETF grant, grandihoidja
1999−2002   
Operaadid, ETF grant, grandihoidja
1999−2002   
Operaadid, Eesti Teadusfondi grant, grandihoidja
1995−1998   
Gerstenhaberi algebra, ETF grant, grandihoidja
1992−1995   
Rahvusvahelise Teadusfondi pikaajalised uurimistoetused, LCROOO ja LL6100, põhitäitja
 
 
Loometöö
Moufangi sümmetria, mitteassotsiatiivne algebra, operaadid, kohomoloogia, vooluringianalüüs

Kvalifikatsioon

Teaduskraadid
Eugen Paal, doktorikraad, 1989, (juh) Jaak Lõhmus, О неассоциативном расширении теоретико-группового метода на основе луп Муфанг и алгебр Мальцева (Rühmateoreetilise meetodi mitteassotsiatiivsest laiendusest Moufangi silmuste ja Maltsevi algebrate baasil), Eesti Teaduste Akadeemia.
 
 
Lisainfo
füüsika-matemaatikakandidaat, 1989, teoreetiline ja matemaatiline füüsika

Lõppenud projektid

Juhendamisel väitekirjad

Juhendatud väitekirjad

Publikatsioonid

Klass
Aasta
Publikatsioon
 
2.1.
2017
Paal, E. (2017). Lineaaralgebra. Tallinn: ASTRALGO.
1.2.
2016
Paal, E. (2016). The one page TELEGRAPH manual. ASTRALGO Science, 2, 1601.
1.2.
2016
Paal, E. (2016). Moufang symmetry I. Associators and Akivis identity. Generalized Lie and Maurer-Cartan equations. ASTRALGO Science, 2, 1602-1−1202-6.
2.1.
2016
Paal, E. (2016). Harilikud diferentsiaalvõrrandid. Tallinn: ASTRALGO.
1.2.
2015
Paal, E; Umbleja, M. (2015). Note on star-triangle equivalence in conducting networks. ASTRALGO Science, 1, 1501-1−1501-4.
1.2.
2015
Paal, E. (2015). q-Tetratransformations in conducting networks. ASTRALGO Science, 1, 1503-1−1503-2.
1.2.
2015
Paal, E.; Umbleja, M (2015). Tetratransformations in conducting networks. ASTRALGO Science, 1, 1502-1−1502-4.
1.2.
2015
Paal, E. (2015). KRON's one page N/W manual. ASTRALGO Science, 1, 1504.
1.2.
2015
Paal, E. (2015). Three graphical operadic compositions for rooted trees. ASTRALGO Science, 1, 1505-1−1505-3.
2.1.
2015
Paal, E. (2015). Matemaatilise füüsika võrrandid. Tallinn: ASTRALGO.
1.1.
2014
Paal, E. (2014). The operadic modeling of gauge systems of the Yang-Mills type. Reports on Mathematical Physics, 74, 109−126.10.1016/S0034-4877(14)60061-6.
3.1.
2014
Makhlouf, A.; Paal, E.; Silvestrov, E.; Stolin, A. (2014). Preface. In: Makhlouf, Abdenacer; Paal, Eugen; Silvestrov, Sergei D.; Stolin, Alexander (Ed.). Algebra, Geometry and Mathematical Physics (vii−ix). . Berlin Heidelberg: Springer Verlag. (Springer Proceedings in Mathematics & Statistics; 85).
3.1.
2014
Paal, Eugen; Kuusk, Piret; Stolin, Alexander (2014). 3Quantum: Algebra Geometry Information. Journal of Physics: Conference Series , 532 (11001), 011001-1−011001-7.
3.1.
2014
Paal, E.; Virkepu, J. (2014). Operadic quantization as a tool for discrete geometry. Journal of Physics: Conference Series , 532 (12023), 012023-1−012023-9.
3.1.
2014
Paal, E.; Umbleja, M. (2014). Note on homological modeling of the electric circuits. Journal of Physics: Conference Series , 532 (12022), 012022-1−012022-7.
4.1.
2014
Paal, E.; Kuusk, P; Stolin, A. (2014). 3Quantum: Algebra Geometry Information (QQQ Conference 2012). Journal of Physics Conference Series, 532. DOI: 10.1088/1742-6596/532/1/011001.
4.1.
2014
Paal, E. (2014). Moduli, Operads, Dynamics II. In: E. Paal (_EditorsAbbr). .Moduli Operads Dynamics II, Tallinn, 3-6 June 2014.
4.1.
2014
Makhlouf, A; Paal, E.; Silvestrov, S. D.; Stolin, A. (2014). Algebra, Geometry and Mathematical Physics. Heidelberg: Springer Verlag. DOI: 10.1007/978-3-642-55361-5.
5.2.
2014
Paal, E.; Umbleja, M. (2014). Homological modelling of the electric circuits. AstrAlgo cWeb, MOD II.
4.1.
2013
Kures, M.; Paal, E. et al (Eds.) (2013). Proceedings of the International Conference "Algebra, Geometry and Mathematical Physics, Brno, 12-14 Sept. 2011". In: .Algebra, Geometry and Mathematical Physics, Brno, 12-14 Sept. 2011.
4.1.
2013
Paal, E.; Vasik, P. (Eds.) (2013). Algebra - Geometry - Mathematical Physics VIII. In: .
4.1.
2013
Paal, E.; Siqveland, A. (Eds.) (2013). Moduli - Operads - Dynamics I. In: .
4.1.
2013
Paal. E. (2013). Graph - Operad - Logic X. AstrAlgo cWeb, 2013.
5.2.
2013
Paal, E. (2013). Operadic Heisenberg-like equation. In: .
3.1.
2012
Abramov, V.; Fuchs, J.; Paal, E.; Shestopalov, Y.; Silvestrov, S. Stolin, A. (2012). Preface to "Algebra, Geometry, and Mathematical Physics 2010". Journal of Physics: Conference Series , 346, 0111001.
3.1.
2012
Paal, E. (2012). Mal'tsev algebras and triality. Journal of Physics: Conference Series , 346, 012015.
4.1.
2012
Stolin, A.; Abramov, V.; Fuchs, J.; , Paal, E.; , Shestopalov, Y.; Silvestrov, S. (2012). Algebra, Geometry, and Mathematical Physics 2010. IOP Publishing Ltd. DOI: 10.1088/1742-6596/346/1/011001.
4.1.
2012
Paal, E.; Zusmanovich, P. (Eds.) (2012). 3Quantum: Algebra - Geometry - Information. In: Paal, E.; Zusmanovich, P. (_EditorsAbbr). Astralgo cWeb.
1.2.
2011
Paal, E.; Virkepu, J. (2011). Jacobi operators of quantum counterparts of three-dimensional real Lie algebras over the harmonic oscillator. Banach Center Publications, 93, 109−209.
1.2.
2011
Makhlouf, A.; Paal, E.; Stolin, A. (2011). Preface to Special Issue On Deformation Theory and Applications. Journal of Generalized Lie Theory and Applications, 5, G110110.
4.1.
2011
(2011). Deformation Theory and Applications. In: Makhlouf, A.; Paal, E., Stolin, A. (_EditorsAbbr). Deformation Theory and Applications..
4.1.
2011
(2011). Mathematical Topics in Quantum Mechanics and Quantum Information. In: Paal, E.; Stolin, A. (_EditorsAbbr). ..
4.1.
2011
(2011). Algebra, Geometry, Mathematical Physics VII. In: Makhlouf, A.; Paal, E. (_EditorsAbbr). ..
4.1.
2011
(2011). Journal of Physical Mathematics. In: Paal, E.; et al (_EditorsAbbr). ..
4.1.
2011
(2011). Journal of Generalized Lie Theory and Applications. In: Paal, E.; et al (_EditorsAbbr). ..
4.1.
2011
Paal, E. (toim.) (2011). Algebra, Geometry and Mathematical Physics. Warszawa: Polish Acad Sciences Inst Mathematics.
6.7.
2011
Abramov, V.; Fuchs, J.; Paal, E.;; Stolin, A.; Tralle, A.; Urbanski, P. (2011). Preface to Proceedings of International Conference "Algebra, Geometry and Mathematical Physics, Stefan Banach International Mathematical Center, 12-16 October, 2009". Banach Center Publications, 93, 5−6.
1.1.
2010
Abramov, V.; Paal, E.; Silvestrov, S.; Stolin, A. (2010). Preface. Special issue devoted to the 4th Baltic–Nordic Workshop “Algebra, Geometry and Mathematical Physics”, Tartu 2008. Proceedings of the Estonian Academy of Sciences, 59 (4), 255.
1.1.
2010
Paal, E.; Virkepu, J. (2010). Quantum counterparts of VIIα, IIIα=1, VIα≠1 over the harmonic oscillator in semiclassical approximation. Proceedings of the Estonian Academy of Sciences, 59 (4), 347−354.
3.4.
2010
Paal, E.; Virkepu, J. (2010). 2D binary operadic Lax representation for harmonic oscillator. In: S. Caenepeel, J. Fuchs, S. Gutt, C. Schweigert, A. Stolin, F. Van Oystayen (_EditorsAbbr). K. Vlaam. Acad. Belgie Wet. Kunsten (KVAB) (209−216).. Brussels: Belgian Mathematical Soc Triomphe.
4.1.
2010
Abramov, V.; Paal, E.; Silvestrov, S.; Stolin, A. (2010). Proceedings of the 4th Baltic-Nordic Workshop "Algebra, Geometry, Mathematical Physics". In: .4th Baltic-Nordic Workshop "Algebra, Geometry, Mathematical Physics", Tartu, 2008. Eesti Teaduste Akadeemia Kirjastus.
4.1.
2010
(2010). Algebra, Geometry, Mathematical Physics VI. In: Paal, E.; Stolin, A. (_EditorsAbbr). ..
4.1.
2010
(2010). Journal of Physical Mathematics. In: Paal, E.; et al (_EditorsAbbr). ..
4.1.
2010
(2010). Journal of Generalized Lie Theory and Applications. Paal, E.; et al...
1.1.
2009
Paal, E.; Virkepu, J. (2009). Quantum counterparts of three-dimensional real Lie algebras over harmonic oscillator. Central European Journal of Physics, 7 pp. DOI: 10.2478/s11534-009-0123-8.
1.1.
2009
Paal, E.; Virkepu, J. (2009). Dynamical deformations of three-dimensional Lie algebras in Bianchi classification over the harmonic oscillator. Journal of Mathematical Physics, 50, 8 pp.
1.2.
2009
Paal, E.; Virkepu, J. (2009). Operadic representations of harmonic oscllator in some 3d algebras. Journal of Generalized Lie Theory and Applications, 3 (1), 53−59.
3.1.
2009
Paal, E.; Virkepu, J. (2009). How to Compose Lagrangian. In: Silvestrov, S.; Paal, E.; Abramov, V.; Stolin, A. (_EditorsAbbr). Generalized Lie Theory in Mathematics, Physics and Beyond (131−140).. Springer.
3.1.
2009
Paal, E. (2009). Moufang transformations and Noether Currents. In: Silvestrov, S.; Paal, E.; Abramov, V.; Stolin, A. (_EditorsAbbr). Generalized Lie Theory in Mathematics, Physics and Beyond (3−8).. Springer.
4.1.
2009
(2009). Algebra, Geometry, Mathematical Physics V. In: Paal, E.; Tralle, A. (_EditorsAbbr). ..
4.1.
2009
(2009). Journal of Physical Mathematics. In: Paal, E.; et al (_EditorsAbbr). ..
4.1.
2009
(2009). Journal of Generalized Lie Theory and Applications. In: Paal, E.; et al (_EditorsAbbr). ..
4.1.
2009
Silvestrov, S.; Paal, E.; Abramov, V.; Stolin, A. (Eds.) (2009). Generalized Lie Theory in Mathematics, Physics and Beyond. Springer.
6.8.
2009
Silvestrov, S.; Paal, E; Abramov, V; Stolin, A. (2009). Preface to book "Generalized Lie Theory in Mathematics, Physics and Beyond". In: Silvestrov, S.; Paal, E; Abramov, V; Stolin, A. (_EditorsAbbr). Generalized Lie Theory in Mathematics, Physics and Beyond (v−vi).. Springer-Verlag Berlin.
1.1.
2008
Paal, E.; Virkepu, J. (2008). Note on operadic harmonic oscillator. Reports on Mathematical Physics, 61 (2), 207−212.
1.2.
2008
Paal, E.; Virkepu, J. (2008). Note on 2d binary operadic harmonic oscillato. Journal of Generalized Lie Theory and Applications, 2 (3), 221−225.
4.1.
2008
(2008). Journal of Generalized Lie Theory and Applications. In: Paal, E.; et al (_EditorsAbbr). ..
4.1.
2008
Abramov, V.; Paal, E.; Silvestrov, S.; Stolin, A. (Eds.) (2008). Journal of Generalized Lie Theory and Applications 2 (2008) 3 : Proceedings of the 3rd Baltic-Nordic Workshop "Algebra, Geometry, and Mathematical Physics, Göteborg, October 11-13, 2007". Tallinn : Astralgo Science.
6.8.
2008
Abramov, V.; Paal, E.; Silvestrov, V; Stolin, A. (2008). Proceedings of the 3rd Baltic-Nordic Workshop "Algebra, Geometry, and Mathematical Physics" in Göteborg, Sweden, October 11-13, 2007, dedicated to memory of Professor Isaiah Kantor (1936-2006). Journal of Generalized Lie Theory and Applications, 2 (3), 109.
1.2.
2007
Paal, E (2007). Invitation to operadic dynamics. Journal of Generalized Lie Theory and Applications, 1 (1), 57−63.
4.1.
2007
Paal, E. (Ed.) (2007). Journal of Generalized Lie Theory and Applications. In: .. [Tallinn].
4.1.
2007
(2007). Algebra, Geometry, Mathematical Physics III. In: Paal, E.; Stolin, A. (_EditorsAbbr). ..
1.1.
2006
Paal, E. (2006). Note on Moufang-Noether currents. Czechoslovak Journal of Physics, 56, 1257−1262. DOI: 10.1007/s10582-006-0434-6.
1.1.
2006
Paal, E. (2006). Note on operadic non-associative deformations. Journal of Nonlinear Mathematical Physics, 13, 87−92. DOI: 10.2991/jnmp.2006.13.s.1.
1.1.
2006
Burdik, Cestmir; Paal, Eugen; Virkepu, Jüri (2006). SO(2) and Hamilton-Dirac mechanics. Journal of Nonlinear Mathematical Physics, 13, 37−43.
3.1.
2006
Paal, E. (2006). Operads and nonassociative deformations. In: Sabinin, L.; Sbitneva, L..; Shestakov, I. (_EditorsAbbr). Non-Associative Algebra and its Applications (323−328).. London - New York: Chapman & Hall. (Monographs and textbooks in pure and applied mathematics; 246).
4.1.
2006
(2006). Proceedings of the Baltic-Nordic Workshop Algebra, Geometry and Mathematical Physics: Tallinn, Estonia, October, 2005. Atlantis Press.
6.8.
2006
Paal, E.; Silvestrov, S. (2006). Proceedings of the Baltic-Nordic Workshop "Algebra, Geometry and Mathematical Physics", Tallinn, Estonia, October, 2005. Journal of Nonlinear Mathematical Physics, 13, 1−2.
1.1.
2005
Paal, E.; Virkepu, R (2005). Plane rotations and Hamilton-Dirac mechanics. Czechoslovak Journal of Physics, 55 (11), 1503−1508.
1.2.
2005
Paal, E. (2005). Operads and deformations. Algebras, Groups and Geometries, 22 (2), 193−200.
1.1.
2004
Paal, E. (2004). Moufang loops and integrability of generalized Lie equations. Czechoslovak Journal of Physics, 54 (11), 1375−1379. DOI: 10.1007/s10582-004-9804-0.
1.2.
2004
Kluge, Liivi; Paal, Eugen (2004). Operads and cohomology. Algebras, Groups and Geometries, 21 (1), 1−8.
1.2.
2004
Paal, E. (2004). Note on analytic Moufang loops. Commentationes mathematicae Universitatis Carolinae, 45 (2), 349−354.
2.4.
2004
Paal, E. (2004). Lineaaralgebra. Tallinn: Tallinna Tehnikaülikooli Kirjastus.
3.1.
2004
Paal, E. (2004). Operads, Cohomology, and Deformations. In: New Developments in Mathematical Physics Research (117−129).. Nova Science Publisher Inc..
1.1.
2003
Paal, E. (2003). Moufang loops and Lie algebras. Czechoslovak Journal of Physics, 53 (11), 1101−1104. DOI: 10.1023/B:CJOP.0000010540.18158.dc.
1.1.
2002
Paal, E. (2002). Operadic deformations as a tool for cogravity. Czechoslovak Journal of Physics, 52 (11), 1277−1282. DOI: 10.1023/A:1021397306799.
1.1.
2002
Kluge, Liivi; Paal, Eugen (2002). Tetracomposition. Communications in Contemporary Mathematics, 4 (3), 435−456.
1.1.
2001
Paal, E. (2001). Operads for x-physics. Czechoslovak Journal of Physics, 51 (12), 1407−1413. DOI: 10.1023/A:1013346709322.
1.1.
2001
Kluge, Liivi; Paal, Eugen (2001). On derivation deviations in an abstract pre-operad. Communications in Algebra, 29 (4), 1609−1626.
1.3.
2001
Kluge, Liivi; Paal, Eugen (2001). Sissejuhatus operaadarvutusse. Eesti Matemaatika Seltsi aastaraamat (13−26).. Tartu: Eesti Matemaatika Selts.
1.1.
2000
Kluge, Liivi; Paal, Eugen; Stasheff, Jim (2000). Invitation to composition. Communications in Algebra, 28 (3), 1405−1422.
2.4.
2000
Paal, E. (2000). Lineaaralgebra elemente. Tallinn: Tallinna Tehnikaülikooli Kirjastus.
2.5.
1999
Paal, E. (1999). Gerstenhaberi algebra : sihtasutuse Eesti Teadusfond grandiprojekti nr. 1453 lõpparuanne : teaduseriala: 1.1. Matemaatika. Tallinn: Tallinna Tehnikaülikool.
1.1.
1998
Lõhmus, L; Paal, E.; Sorgsepp, L. (1998). About nonassociativity in mathematics and physics. Acta Applicandae Mathematicae, 50, 3−31. DOI: 10.1023/A:1005854831381.
1.1.
1998
Paal, E. (1998). Continuous Moufang transformations. Acta Applicandae Mathematicae, 50, 77−91. DOI: 10.1023/A:1005811017268.
1.1.
1998
Kuusk, P.; Paal, E. (1998). Some applications of geodesic loops and nonlinear geometric algebra in the theory of gravity. Acta Applicandae Mathematicae, 50, 67−76.
1.2.
1998
Paal, E. (1998). Coassociativity, cohomology and Gerstenhaber algebras. Algebras, Groups and Geometries, 15 (1), 85−93.
1.1.
1997
Kuusk, P.; Ord, J.; Paal, E. (1997). Quantum kinematics of a test particle in a curved spacetime. Classical and Quantum Gravity, 14 (10), 2917−2926.
1.1.
1996
Kuusk, P.; Paal, E. (1996). Geodesic multiplication and BRST-like operators. General Relativity and Gravitation, 28 (8), 991−998.
1.2.
1996
Kuusk, P; Paal, E. (1996). Local differentiable loops and BRST-like cohomology. Algebras, Groups and Geometries, 13 (4), 465−469.
1.1.
1995
Oziewicz, Z.; Paal, E.; Rozanski, J. (1995). Derivations in braided geometry. Acta Physica Polonica B, 26 (7), 1253−1273.
1.2.
1995
Kuus, P.; Örd, J.; Paal, E. (1995). Geodesic multiplication and geometrical BRST-like operators. Proceedings of the Estonian Academy of Sciences. Physics. Mathematics, 44 (4), 437−449.
1.2.
1995
Kuusk, P.; Paal, E. (1995). Geodesic loops and BRST-like cohomology. Proceedings of the Estonian Academy of Sciences. Physics. Mathematics, 45, 128−133.
3.1.
1995
Lõhmus, L.; Paal, E.; Sorgsepp, L. (1995). Mal'tsev algebras and conservation laws. In: L. A. Bokut′, A. I. Kostrikin, S. S. Kutateladze (_EditorsAbbr). Second International Conference on Algebra Dedicated to the Memory of A, I, Shirshov Proceedings of the Second International Conference on Algebra August 20-25, 1991 Barnaul, Russia (281−290).. American Mathematical Society. (Contemporary Mathematics; 184).
1.1.
1994
Kuusk, P.; Ord, J.; Paal, E. (1994). Geodesic multiplication and the theory of gravity. Journal of Mathematical Physics, 35 (1), 321−334.
2.1.
1994
Lõhmus, J; Paal, E.; Sorgsepp, L. (1994). Nonassociative Algebras in Physics. Palm Harbor, U.S.A: Hadronic Press.
3.1.
1994
Oziewicz, Z.; Paal, E.; Rozanski, J. (1994). Coalgebra and cohomology. In: Gonzalez, S. (_EditorsAbbr). Non-associative Algebra and its Applications (314−322).. Kluwer Academic Publishers.
3.2.
1994
Paal, E. (1994). Birepresentations of Mal'tsev algebras. In: Vichmann, F., etc. (_EditorsAbbr). Matemaatika. Füüsika = B, Mathematics. Physics (19−32).. Tallinn: Tallinna Tehnikaülikool. (Tallinna Tehnikaülikooli toimetised = Transactions of Tallinn Technical University = Труды Таллиннского технического университета; 738 B).
3.4.
1994
Kuusk, P.; Paal, E. (1994). Geodesic multiplication in the theory of gravity. In: Yu. N. Gnedin, A. A. Grib, V. M. Mostepanenko (_EditorsAbbr). Proc. Second Alexander Friedmann Int. Seminar on Grav. and Cosmology (324−335).. St. Petersburg: Russian Academy of Sciences.
1.2.
1993
Paal, E. (1993). Moufang-Mal'tsev symmetry. Proceedings of the Estonian Academy of Sciences, 42, 157−165.
3.1.
1993
Lõhmus, L.; Paal, E.; Sorgsepp, L. (1993). Moufang loopsa and conservation laws. In: H. D. Doebner, W. Scherer, F. Schroeck, Jr. (_EditorsAbbr). Classical and Quantum Systems - Foundations and Symmetries : Proceedings of the !1 International Wigner Symposium : Goslar, Germany July 16 - 20, 1991 (330−333).. Singapore: World Scientific.
1.2.
1992
Paal, E. (1992). Moufang loops and generalized Lie equations. Proceedings of the Estonian Academy of Sciences. Physics. Mathematics, 41 (2), 125−132.
1.2.
1992
Lõhmus, J.; Paal, E.; Sorgsepp, L. (1992). Moufang symmetries and conservation laws. Proceedings of the Estonian Academy of Sciences, 41, 133−141.
1.2.
1992
Paal, E. (1992). Mal'tsev algebras and generalized Lie equations. Webs and Quasigroups, 1992, 69−78.
3.2.
1992
Kuusk, P.; Paal, E. (1992). Geodesic multiplication as a tool for classical and quantum gravity. In: Matemaatika. Füüsika = B, Mathematics. Physics (33−42).. Tallinn: Tallinna Tehnikaülikool. (Tallinna Tehnikaülikooli toimetised = Transactions of Tallinn Technical University = Труды Таллиннского технического университета; 733 B).
1.2.
1991
Paal, E. (1991). Birepresentations of derivative Moufang loops. Proceedings of the Estonian Academy of Sciences, 40, 105−111.
3.1.
1991
Paal, E. (1991). Derivative Moufang transformations. In: Dodonov, V. V.; Man'ko, V. I. (_EditorsAbbr). Group Theoretical Methods in Physics (573−574).. Springer. (Lecture Notes in Physics; 382).
5.2.
1991
Paal, E. (1991). Birepresentations of Mal'tsev algebras. Abstr. of Second Int. Conf. on Algebra Dedicated to A. I. Shirshov: Second International Conference on Algebra, Dedicated to A. I. Shirshov, Barnaul, Aug. 20-25, 1991. Russian Academy of Sciences,.
1.3.
1990
Lõhmus, J. Paal, E. Sorgsepp, L. (1990). Nonassociativity in mathematics and physics. Füüsika Instituudi uurimused, 66, 8−22.
3.2.
1990
Paal, E. (1990). On invariants of continuous Moufang transformations. In: Я. Лыхмус, П. Кууск (_EditorsAbbr). Квазигруппы и неассоциативные алгебры в физике (98−106).. Тарту: Академия наук Эстонской ССР. (Труды Института физики Академии наук Эстонской ССР; 66).
5.2.
1990
Paal, E. (1990). Derivative birepresentations of Moufang loops. In: Matemaatika teoreetilisi ja rakenduslikke küsimusi = Problems of pure and applied mathematics : konverentsi ettekannete teesid, 21-22.09.1990 (15−16).. Tartu: Tartu University Press.
2.5.
1989
Lõhmus, J.; Paal, E.; Sorgsepp, L. (1989). On currents and symmetries associated with Mal'tsev algebras. Tartu: Academy of Sciences of the Estonian S.S.R..
3.2.
1989
Paal, E. (1989). On bicombinatorial representation of the Moufang loops. И. Отс, В. Розенгаус. Фундаментальные поля (104−124).. Тарту : Академия наук Эстонской ССР. (Труды Института физики Академий наук Эстонской ССР ; 64).
5.2.
1989
Paal, E. (1989). On a Nonassociative Extension of Group Theoretical Method Based on Moufang Loops and Mal'tsev Algebras. Theory of Models and Algebras. Int. Con. on Algebra Dedicated to A. I. Mal'tsev, Novosibirsk, Aug. 21-26, 1989: Int. Con. on Algebra Dedicated to A. I. Mal'tsev, Novosibirsk, Aug. 21-26, 1989. Novisibirsk: Russian Academy of Sciences, 97.
6.7.
1989
Paal, E. (1989). On a Nonassociative Extension of Group Theoretical Method Based on Moufang Loops and Mal'tsev Algebras. (Doktoritöö, Eesti Teaduste Akadeemia). Eesti Teaduste Akadeemia.
6.7.
1989
Lõhmus, J.; Paal, E.; Sorgsepp, L. (1989). On Currents and Symmetries Associated with Mal'tsev Algebras. In: .. Tartu: Academy of Sciences of the Estonian S.S.R.. (Preprint / Academy of Sciences of the Estonian S.S.R., section of Physics and Astronomy; F-50).
2.5.
1988
Paal, E. (1988). Analytic Moufang-transformations. Tartu: Academy of Sciences of the Estonian S.S.R..
6.7.
1988
Paal, E. (1988). Analytic Moufang Transformations. In: .. Tartu: Academy of Sciences of the Estonian S.S.R.. (Preprint / Academy of Sciences of the Estonian S.S.R., Section of Physics and Astronomy; F-46).
2.5.
1987
Паал, Э. (1987). Введение в Муфанг-симметрию. . Тарту : Академия наук Эстонской ССР. (Препринт / Академия наук Эстонской ССР, отделение физики и астрономии; F-42).
3.2.
1987
Paal, E. (1987). Moufang transformations. П. Кууск и Я. Лыхмус. Фундаментальные взаимодействия (142−158).. Тарту : Академия Наук ЭССР. (Труды Института физики / Академия наук ЭССР; 62).
26.11.2018

Eugen Paal

https://www.etis.ee/CV/Paal_E/eng

Career

Institutions and positions
2005–...   
ASTRALGO R&D, Visiting Researcher (0,50)
1998–2017   
Tallinn University of Technology, Professor of Mathematical Physics (1,00)
 
 
Education
1986–1988   
PhD studies, Particle Theory Group at Institute of Physics, Estonian Academy of Sciences
1972–1977   
Theoretical and mathematical physics, Faculty of Physics and Chemistry, Universtity of Tartu
 
 
R&D related managerial and administrative work
2012−...   
Tallinn conference deputy
2005−...   
ASTRALGO R&D; board member
2004−...   
ISQS network, board member
2002−...   
AGMP network, cofounder, board member, coordinator
2014−2015   
In. Conf. Moduli - Operads - Dynamics (MOD) II, 03 - 06 June 2014, Tallinn, Estonia, organizer
2013−2014   
Int. Conf. Moduli - Operads - Dynamics (MOD) I, 09-11 July 2013, Kongsberg, Norway, co-organizer
2012−2014   
Int. Conf. AGMP VIII, 09-12 Sept. 2012, Brno, Czech Republic, co-organizer
2012−2014   
Satellite Conf. of 6th European Mathematical Congress (ECM6), 3Quantum: Algebra - Geometry - Information, 10-13 July 2012, Tallinn, Estonia, organizer
2012−2015   
Operads, Deformations, Dynamics, Estonian SF Grant, grant holder
2012−2015   
Operads, deformations, dynamics, Estonian SF Grant, grant holder
2011−2012   
AGMP & MP2 Int. Summer School, Mathematical Topics in Quantum Mechanics and Quantum Information, 05-09 Sept. 2011, Tjärnö, Sweden, co-organizer
2011−2014   
Int. Conf. AGMP VII, 24-16 Oct. 2011, Mulhouse, France, co-organizer
2010−2012   
Int. Conf. AGMP VI, 25.-30. Oct. 2010, Tjärnö, Sweden, co-organizer
2009−2011   
Int. Conf. AGMP V, 12-16 Oct. 2009, Banach Conf. Center, Bedlewo, Poland, co-organizer
2009−2014   
J. Phys. Math., founding editor, editor-in-chief (2009-2014)
2008−2010   
Int. Conf. AGMP IV, 09-11 Oct. 2008, Tartu, Estonia, co-organizer
2007−2008   
Int. Conf. AGMP III, 11-13 Oct. 2007, Göteborg, Sweden, co-organizer
2007−2010   
Generalized Lie Theory, Estonian SF Grant, grant holder
2007−2010   
Generalized Lie Theory, Estonian SF Grant, grant holder
2006−2011   
Astralgo CC & Eugen Paal (FIE)
2006−2009   
Int. Conf. AGMP II, 12-14 Oct. 2006, Lund, Sweden, co-organizer
2006−2014   
J. Gen. Lie Theory Appl., founding editor and publisher, editor-in-chief (2006-2014)
2005−2006   
Int. conf. AGMP I, 8 Oct. 2005, Tallinn, Estonia, organizer
2003−2006   
Operads and Cohomology, Estonian SF Grant, grant holder
1999−2002   
Operads, Estonian SF Grant, grant holder
1999−2002   
Operads, Estonian SF Grant, grant holder
1995−1998   
Gerstenhaber Algebra, Estonian SF Grant, grant holder
1992−1995   
Int. Sci. Found. Long-term Research Grants, LCROOO ja LL6100, co-investigator
 
 
Creative work
Moufang symmetry, nonassociative algebra, operads, cohomology, circuit analyses

Qualifications

Academic degrees
Eugen Paal, Doctor's Degree, 1989, (sup) Jaak Lõhmus, О неассоциативном расширении теоретико-группового метода на основе луп Муфанг и алгебр Мальцева (About a Non-Associative Extension of the Group Theoretical Method Based on Moufang Loops and Mal'tsev Algebras), Estonian Academy of Sciences.
 
 
Additional information
PhD, 1989, theoretical and mathematical physics

Completed projects

Dissertations under supervision

Supervised dissertations

Publications

Category
Year
Publication
 
2.1.
2017
Paal, E. (2017). Lineaaralgebra. Tallinn: ASTRALGO.
1.2.
2016
Paal, E. (2016). The one page TELEGRAPH manual. ASTRALGO Science, 2, 1601.
1.2.
2016
Paal, E. (2016). Moufang symmetry I. Associators and Akivis identity. Generalized Lie and Maurer-Cartan equations. ASTRALGO Science, 2, 1602-1−1202-6.
2.1.
2016
Paal, E. (2016). Harilikud diferentsiaalvõrrandid. Tallinn: ASTRALGO.
1.2.
2015
Paal, E; Umbleja, M. (2015). Note on star-triangle equivalence in conducting networks. ASTRALGO Science, 1, 1501-1−1501-4.
1.2.
2015
Paal, E. (2015). q-Tetratransformations in conducting networks. ASTRALGO Science, 1, 1503-1−1503-2.
1.2.
2015
Paal, E.; Umbleja, M (2015). Tetratransformations in conducting networks. ASTRALGO Science, 1, 1502-1−1502-4.
1.2.
2015
Paal, E. (2015). KRON's one page N/W manual. ASTRALGO Science, 1, 1504.
1.2.
2015
Paal, E. (2015). Three graphical operadic compositions for rooted trees. ASTRALGO Science, 1, 1505-1−1505-3.
2.1.
2015
Paal, E. (2015). Matemaatilise füüsika võrrandid. Tallinn: ASTRALGO.
1.1.
2014
Paal, E. (2014). The operadic modeling of gauge systems of the Yang-Mills type. Reports on Mathematical Physics, 74, 109−126.10.1016/S0034-4877(14)60061-6.
3.1.
2014
Makhlouf, A.; Paal, E.; Silvestrov, E.; Stolin, A. (2014). Preface. In: Makhlouf, Abdenacer; Paal, Eugen; Silvestrov, Sergei D.; Stolin, Alexander (Ed.). Algebra, Geometry and Mathematical Physics (vii−ix). . Berlin Heidelberg: Springer Verlag. (Springer Proceedings in Mathematics & Statistics; 85).
3.1.
2014
Paal, Eugen; Kuusk, Piret; Stolin, Alexander (2014). 3Quantum: Algebra Geometry Information. Journal of Physics: Conference Series , 532 (11001), 011001-1−011001-7.
3.1.
2014
Paal, E.; Virkepu, J. (2014). Operadic quantization as a tool for discrete geometry. Journal of Physics: Conference Series , 532 (12023), 012023-1−012023-9.
3.1.
2014
Paal, E.; Umbleja, M. (2014). Note on homological modeling of the electric circuits. Journal of Physics: Conference Series , 532 (12022), 012022-1−012022-7.
4.1.
2014
Paal, E.; Kuusk, P; Stolin, A. (2014). 3Quantum: Algebra Geometry Information (QQQ Conference 2012). Journal of Physics Conference Series, 532. DOI: 10.1088/1742-6596/532/1/011001.
4.1.
2014
Paal, E. (2014). Moduli, Operads, Dynamics II. In: E. Paal (_EditorsAbbr). .Moduli Operads Dynamics II, Tallinn, 3-6 June 2014.
4.1.
2014
Makhlouf, A; Paal, E.; Silvestrov, S. D.; Stolin, A. (2014). Algebra, Geometry and Mathematical Physics. Heidelberg: Springer Verlag. DOI: 10.1007/978-3-642-55361-5.
5.2.
2014
Paal, E.; Umbleja, M. (2014). Homological modelling of the electric circuits. AstrAlgo cWeb, MOD II.
4.1.
2013
Kures, M.; Paal, E. et al (Eds.) (2013). Proceedings of the International Conference "Algebra, Geometry and Mathematical Physics, Brno, 12-14 Sept. 2011". In: .Algebra, Geometry and Mathematical Physics, Brno, 12-14 Sept. 2011.
4.1.
2013
Paal, E.; Vasik, P. (Eds.) (2013). Algebra - Geometry - Mathematical Physics VIII. In: .
4.1.
2013
Paal, E.; Siqveland, A. (Eds.) (2013). Moduli - Operads - Dynamics I. In: .
4.1.
2013
Paal. E. (2013). Graph - Operad - Logic X. AstrAlgo cWeb, 2013.
5.2.
2013
Paal, E. (2013). Operadic Heisenberg-like equation. In: .
3.1.
2012
Abramov, V.; Fuchs, J.; Paal, E.; Shestopalov, Y.; Silvestrov, S. Stolin, A. (2012). Preface to "Algebra, Geometry, and Mathematical Physics 2010". Journal of Physics: Conference Series , 346, 0111001.
3.1.
2012
Paal, E. (2012). Mal'tsev algebras and triality. Journal of Physics: Conference Series , 346, 012015.
4.1.
2012
Stolin, A.; Abramov, V.; Fuchs, J.; , Paal, E.; , Shestopalov, Y.; Silvestrov, S. (2012). Algebra, Geometry, and Mathematical Physics 2010. IOP Publishing Ltd. DOI: 10.1088/1742-6596/346/1/011001.
4.1.
2012
Paal, E.; Zusmanovich, P. (Eds.) (2012). 3Quantum: Algebra - Geometry - Information. In: Paal, E.; Zusmanovich, P. (_EditorsAbbr). Astralgo cWeb.
1.2.
2011
Paal, E.; Virkepu, J. (2011). Jacobi operators of quantum counterparts of three-dimensional real Lie algebras over the harmonic oscillator. Banach Center Publications, 93, 109−209.
1.2.
2011
Makhlouf, A.; Paal, E.; Stolin, A. (2011). Preface to Special Issue On Deformation Theory and Applications. Journal of Generalized Lie Theory and Applications, 5, G110110.
4.1.
2011
(2011). Deformation Theory and Applications. In: Makhlouf, A.; Paal, E., Stolin, A. (_EditorsAbbr). Deformation Theory and Applications..
4.1.
2011
(2011). Mathematical Topics in Quantum Mechanics and Quantum Information. In: Paal, E.; Stolin, A. (_EditorsAbbr). ..
4.1.
2011
(2011). Algebra, Geometry, Mathematical Physics VII. In: Makhlouf, A.; Paal, E. (_EditorsAbbr). ..
4.1.
2011
(2011). Journal of Physical Mathematics. In: Paal, E.; et al (_EditorsAbbr). ..
4.1.
2011
(2011). Journal of Generalized Lie Theory and Applications. In: Paal, E.; et al (_EditorsAbbr). ..
4.1.
2011
Paal, E. (toim.) (2011). Algebra, Geometry and Mathematical Physics. Warszawa: Polish Acad Sciences Inst Mathematics.
6.7.
2011
Abramov, V.; Fuchs, J.; Paal, E.;; Stolin, A.; Tralle, A.; Urbanski, P. (2011). Preface to Proceedings of International Conference "Algebra, Geometry and Mathematical Physics, Stefan Banach International Mathematical Center, 12-16 October, 2009". Banach Center Publications, 93, 5−6.
1.1.
2010
Abramov, V.; Paal, E.; Silvestrov, S.; Stolin, A. (2010). Preface. Special issue devoted to the 4th Baltic–Nordic Workshop “Algebra, Geometry and Mathematical Physics”, Tartu 2008. Proceedings of the Estonian Academy of Sciences, 59 (4), 255.
1.1.
2010
Paal, E.; Virkepu, J. (2010). Quantum counterparts of VIIα, IIIα=1, VIα≠1 over the harmonic oscillator in semiclassical approximation. Proceedings of the Estonian Academy of Sciences, 59 (4), 347−354.
3.4.
2010
Paal, E.; Virkepu, J. (2010). 2D binary operadic Lax representation for harmonic oscillator. In: S. Caenepeel, J. Fuchs, S. Gutt, C. Schweigert, A. Stolin, F. Van Oystayen (_EditorsAbbr). K. Vlaam. Acad. Belgie Wet. Kunsten (KVAB) (209−216).. Brussels: Belgian Mathematical Soc Triomphe.
4.1.
2010
Abramov, V.; Paal, E.; Silvestrov, S.; Stolin, A. (2010). Proceedings of the 4th Baltic-Nordic Workshop "Algebra, Geometry, Mathematical Physics". In: .4th Baltic-Nordic Workshop "Algebra, Geometry, Mathematical Physics", Tartu, 2008. Eesti Teaduste Akadeemia Kirjastus.
4.1.
2010
(2010). Algebra, Geometry, Mathematical Physics VI. In: Paal, E.; Stolin, A. (_EditorsAbbr). ..
4.1.
2010
(2010). Journal of Physical Mathematics. In: Paal, E.; et al (_EditorsAbbr). ..
4.1.
2010
(2010). Journal of Generalized Lie Theory and Applications. Paal, E.; et al...
1.1.
2009
Paal, E.; Virkepu, J. (2009). Quantum counterparts of three-dimensional real Lie algebras over harmonic oscillator. Central European Journal of Physics, 7 pp. DOI: 10.2478/s11534-009-0123-8.
1.1.
2009
Paal, E.; Virkepu, J. (2009). Dynamical deformations of three-dimensional Lie algebras in Bianchi classification over the harmonic oscillator. Journal of Mathematical Physics, 50, 8 pp.
1.2.
2009
Paal, E.; Virkepu, J. (2009). Operadic representations of harmonic oscllator in some 3d algebras. Journal of Generalized Lie Theory and Applications, 3 (1), 53−59.
3.1.
2009
Paal, E.; Virkepu, J. (2009). How to Compose Lagrangian. In: Silvestrov, S.; Paal, E.; Abramov, V.; Stolin, A. (_EditorsAbbr). Generalized Lie Theory in Mathematics, Physics and Beyond (131−140).. Springer.
3.1.
2009
Paal, E. (2009). Moufang transformations and Noether Currents. In: Silvestrov, S.; Paal, E.; Abramov, V.; Stolin, A. (_EditorsAbbr). Generalized Lie Theory in Mathematics, Physics and Beyond (3−8).. Springer.
4.1.
2009
(2009). Algebra, Geometry, Mathematical Physics V. In: Paal, E.; Tralle, A. (_EditorsAbbr). ..
4.1.
2009
(2009). Journal of Physical Mathematics. In: Paal, E.; et al (_EditorsAbbr). ..
4.1.
2009
(2009). Journal of Generalized Lie Theory and Applications. In: Paal, E.; et al (_EditorsAbbr). ..
4.1.
2009
Silvestrov, S.; Paal, E.; Abramov, V.; Stolin, A. (Eds.) (2009). Generalized Lie Theory in Mathematics, Physics and Beyond. Springer.
6.8.
2009
Silvestrov, S.; Paal, E; Abramov, V; Stolin, A. (2009). Preface to book "Generalized Lie Theory in Mathematics, Physics and Beyond". In: Silvestrov, S.; Paal, E; Abramov, V; Stolin, A. (_EditorsAbbr). Generalized Lie Theory in Mathematics, Physics and Beyond (v−vi).. Springer-Verlag Berlin.
1.1.
2008
Paal, E.; Virkepu, J. (2008). Note on operadic harmonic oscillator. Reports on Mathematical Physics, 61 (2), 207−212.
1.2.
2008
Paal, E.; Virkepu, J. (2008). Note on 2d binary operadic harmonic oscillato. Journal of Generalized Lie Theory and Applications, 2 (3), 221−225.
4.1.
2008
(2008). Journal of Generalized Lie Theory and Applications. In: Paal, E.; et al (_EditorsAbbr). ..
4.1.
2008
Abramov, V.; Paal, E.; Silvestrov, S.; Stolin, A. (Eds.) (2008). Journal of Generalized Lie Theory and Applications 2 (2008) 3 : Proceedings of the 3rd Baltic-Nordic Workshop "Algebra, Geometry, and Mathematical Physics, Göteborg, October 11-13, 2007". Tallinn : Astralgo Science.
6.8.
2008
Abramov, V.; Paal, E.; Silvestrov, V; Stolin, A. (2008). Proceedings of the 3rd Baltic-Nordic Workshop "Algebra, Geometry, and Mathematical Physics" in Göteborg, Sweden, October 11-13, 2007, dedicated to memory of Professor Isaiah Kantor (1936-2006). Journal of Generalized Lie Theory and Applications, 2 (3), 109.
1.2.
2007
Paal, E (2007). Invitation to operadic dynamics. Journal of Generalized Lie Theory and Applications, 1 (1), 57−63.
4.1.
2007
Paal, E. (Ed.) (2007). Journal of Generalized Lie Theory and Applications. In: .. [Tallinn].
4.1.
2007
(2007). Algebra, Geometry, Mathematical Physics III. In: Paal, E.; Stolin, A. (_EditorsAbbr). ..
1.1.
2006
Paal, E. (2006). Note on Moufang-Noether currents. Czechoslovak Journal of Physics, 56, 1257−1262. DOI: 10.1007/s10582-006-0434-6.
1.1.
2006
Paal, E. (2006). Note on operadic non-associative deformations. Journal of Nonlinear Mathematical Physics, 13, 87−92. DOI: 10.2991/jnmp.2006.13.s.1.
1.1.
2006
Burdik, Cestmir; Paal, Eugen; Virkepu, Jüri (2006). SO(2) and Hamilton-Dirac mechanics. Journal of Nonlinear Mathematical Physics, 13, 37−43.
3.1.
2006
Paal, E. (2006). Operads and nonassociative deformations. In: Sabinin, L.; Sbitneva, L..; Shestakov, I. (_EditorsAbbr). Non-Associative Algebra and its Applications (323−328).. London - New York: Chapman & Hall. (Monographs and textbooks in pure and applied mathematics; 246).
4.1.
2006
(2006). Proceedings of the Baltic-Nordic Workshop Algebra, Geometry and Mathematical Physics: Tallinn, Estonia, October, 2005. Atlantis Press.
6.8.
2006
Paal, E.; Silvestrov, S. (2006). Proceedings of the Baltic-Nordic Workshop "Algebra, Geometry and Mathematical Physics", Tallinn, Estonia, October, 2005. Journal of Nonlinear Mathematical Physics, 13, 1−2.
1.1.
2005
Paal, E.; Virkepu, R (2005). Plane rotations and Hamilton-Dirac mechanics. Czechoslovak Journal of Physics, 55 (11), 1503−1508.
1.2.
2005
Paal, E. (2005). Operads and deformations. Algebras, Groups and Geometries, 22 (2), 193−200.
1.1.
2004
Paal, E. (2004). Moufang loops and integrability of generalized Lie equations. Czechoslovak Journal of Physics, 54 (11), 1375−1379. DOI: 10.1007/s10582-004-9804-0.
1.2.
2004
Kluge, Liivi; Paal, Eugen (2004). Operads and cohomology. Algebras, Groups and Geometries, 21 (1), 1−8.
1.2.
2004
Paal, E. (2004). Note on analytic Moufang loops. Commentationes mathematicae Universitatis Carolinae, 45 (2), 349−354.
2.4.
2004
Paal, E. (2004). Lineaaralgebra. Tallinn: Tallinna Tehnikaülikooli Kirjastus.
3.1.
2004
Paal, E. (2004). Operads, Cohomology, and Deformations. In: New Developments in Mathematical Physics Research (117−129).. Nova Science Publisher Inc..
1.1.
2003
Paal, E. (2003). Moufang loops and Lie algebras. Czechoslovak Journal of Physics, 53 (11), 1101−1104. DOI: 10.1023/B:CJOP.0000010540.18158.dc.
1.1.
2002
Paal, E. (2002). Operadic deformations as a tool for cogravity. Czechoslovak Journal of Physics, 52 (11), 1277−1282. DOI: 10.1023/A:1021397306799.
1.1.
2002
Kluge, Liivi; Paal, Eugen (2002). Tetracomposition. Communications in Contemporary Mathematics, 4 (3), 435−456.
1.1.
2001
Paal, E. (2001). Operads for x-physics. Czechoslovak Journal of Physics, 51 (12), 1407−1413. DOI: 10.1023/A:1013346709322.
1.1.
2001
Kluge, Liivi; Paal, Eugen (2001). On derivation deviations in an abstract pre-operad. Communications in Algebra, 29 (4), 1609−1626.
1.3.
2001
Kluge, Liivi; Paal, Eugen (2001). Sissejuhatus operaadarvutusse. Eesti Matemaatika Seltsi aastaraamat (13−26).. Tartu: Eesti Matemaatika Selts.
1.1.
2000
Kluge, Liivi; Paal, Eugen; Stasheff, Jim (2000). Invitation to composition. Communications in Algebra, 28 (3), 1405−1422.
2.4.
2000
Paal, E. (2000). Lineaaralgebra elemente. Tallinn: Tallinna Tehnikaülikooli Kirjastus.
2.5.
1999
Paal, E. (1999). Gerstenhaberi algebra : sihtasutuse Eesti Teadusfond grandiprojekti nr. 1453 lõpparuanne : teaduseriala: 1.1. Matemaatika. Tallinn: Tallinna Tehnikaülikool.
1.1.
1998
Lõhmus, L; Paal, E.; Sorgsepp, L. (1998). About nonassociativity in mathematics and physics. Acta Applicandae Mathematicae, 50, 3−31. DOI: 10.1023/A:1005854831381.
1.1.
1998
Paal, E. (1998). Continuous Moufang transformations. Acta Applicandae Mathematicae, 50, 77−91. DOI: 10.1023/A:1005811017268.
1.1.
1998
Kuusk, P.; Paal, E. (1998). Some applications of geodesic loops and nonlinear geometric algebra in the theory of gravity. Acta Applicandae Mathematicae, 50, 67−76.
1.2.
1998
Paal, E. (1998). Coassociativity, cohomology and Gerstenhaber algebras. Algebras, Groups and Geometries, 15 (1), 85−93.
1.1.
1997
Kuusk, P.; Ord, J.; Paal, E. (1997). Quantum kinematics of a test particle in a curved spacetime. Classical and Quantum Gravity, 14 (10), 2917−2926.
1.1.
1996
Kuusk, P.; Paal, E. (1996). Geodesic multiplication and BRST-like operators. General Relativity and Gravitation, 28 (8), 991−998.
1.2.
1996
Kuusk, P; Paal, E. (1996). Local differentiable loops and BRST-like cohomology. Algebras, Groups and Geometries, 13 (4), 465−469.
1.1.
1995
Oziewicz, Z.; Paal, E.; Rozanski, J. (1995). Derivations in braided geometry. Acta Physica Polonica B, 26 (7), 1253−1273.
1.2.
1995
Kuus, P.; Örd, J.; Paal, E. (1995). Geodesic multiplication and geometrical BRST-like operators. Proceedings of the Estonian Academy of Sciences. Physics. Mathematics, 44 (4), 437−449.
1.2.
1995
Kuusk, P.; Paal, E. (1995). Geodesic loops and BRST-like cohomology. Proceedings of the Estonian Academy of Sciences. Physics. Mathematics, 45, 128−133.
3.1.
1995
Lõhmus, L.; Paal, E.; Sorgsepp, L. (1995). Mal'tsev algebras and conservation laws. In: L. A. Bokut′, A. I. Kostrikin, S. S. Kutateladze (_EditorsAbbr). Second International Conference on Algebra Dedicated to the Memory of A, I, Shirshov Proceedings of the Second International Conference on Algebra August 20-25, 1991 Barnaul, Russia (281−290).. American Mathematical Society. (Contemporary Mathematics; 184).
1.1.
1994
Kuusk, P.; Ord, J.; Paal, E. (1994). Geodesic multiplication and the theory of gravity. Journal of Mathematical Physics, 35 (1), 321−334.
2.1.
1994
Lõhmus, J; Paal, E.; Sorgsepp, L. (1994). Nonassociative Algebras in Physics. Palm Harbor, U.S.A: Hadronic Press.
3.1.
1994
Oziewicz, Z.; Paal, E.; Rozanski, J. (1994). Coalgebra and cohomology. In: Gonzalez, S. (_EditorsAbbr). Non-associative Algebra and its Applications (314−322).. Kluwer Academic Publishers.
3.2.
1994
Paal, E. (1994). Birepresentations of Mal'tsev algebras. In: Vichmann, F., etc. (_EditorsAbbr). Matemaatika. Füüsika = B, Mathematics. Physics (19−32).. Tallinn: Tallinna Tehnikaülikool. (Tallinna Tehnikaülikooli toimetised = Transactions of Tallinn Technical University = Труды Таллиннского технического университета; 738 B).
3.4.
1994
Kuusk, P.; Paal, E. (1994). Geodesic multiplication in the theory of gravity. In: Yu. N. Gnedin, A. A. Grib, V. M. Mostepanenko (_EditorsAbbr). Proc. Second Alexander Friedmann Int. Seminar on Grav. and Cosmology (324−335).. St. Petersburg: Russian Academy of Sciences.
1.2.
1993
Paal, E. (1993). Moufang-Mal'tsev symmetry. Proceedings of the Estonian Academy of Sciences, 42, 157−165.
3.1.
1993
Lõhmus, L.; Paal, E.; Sorgsepp, L. (1993). Moufang loopsa and conservation laws. In: H. D. Doebner, W. Scherer, F. Schroeck, Jr. (_EditorsAbbr). Classical and Quantum Systems - Foundations and Symmetries : Proceedings of the !1 International Wigner Symposium : Goslar, Germany July 16 - 20, 1991 (330−333).. Singapore: World Scientific.
1.2.
1992
Paal, E. (1992). Moufang loops and generalized Lie equations. Proceedings of the Estonian Academy of Sciences. Physics. Mathematics, 41 (2), 125−132.
1.2.
1992
Lõhmus, J.; Paal, E.; Sorgsepp, L. (1992). Moufang symmetries and conservation laws. Proceedings of the Estonian Academy of Sciences, 41, 133−141.
1.2.
1992
Paal, E. (1992). Mal'tsev algebras and generalized Lie equations. Webs and Quasigroups, 1992, 69−78.
3.2.
1992
Kuusk, P.; Paal, E. (1992). Geodesic multiplication as a tool for classical and quantum gravity. In: Matemaatika. Füüsika = B, Mathematics. Physics (33−42).. Tallinn: Tallinna Tehnikaülikool. (Tallinna Tehnikaülikooli toimetised = Transactions of Tallinn Technical University = Труды Таллиннского технического университета; 733 B).
1.2.
1991
Paal, E. (1991). Birepresentations of derivative Moufang loops. Proceedings of the Estonian Academy of Sciences, 40, 105−111.
3.1.
1991
Paal, E. (1991). Derivative Moufang transformations. In: Dodonov, V. V.; Man'ko, V. I. (_EditorsAbbr). Group Theoretical Methods in Physics (573−574).. Springer. (Lecture Notes in Physics; 382).
5.2.
1991
Paal, E. (1991). Birepresentations of Mal'tsev algebras. Abstr. of Second Int. Conf. on Algebra Dedicated to A. I. Shirshov: Second International Conference on Algebra, Dedicated to A. I. Shirshov, Barnaul, Aug. 20-25, 1991. Russian Academy of Sciences,.
1.3.
1990
Lõhmus, J. Paal, E. Sorgsepp, L. (1990). Nonassociativity in mathematics and physics. Füüsika Instituudi uurimused, 66, 8−22.
3.2.
1990
Paal, E. (1990). On invariants of continuous Moufang transformations. In: Я. Лыхмус, П. Кууск (_EditorsAbbr). Квазигруппы и неассоциативные алгебры в физике (98−106).. Тарту: Академия наук Эстонской ССР. (Труды Института физики Академии наук Эстонской ССР; 66).
5.2.
1990
Paal, E. (1990). Derivative birepresentations of Moufang loops. In: Matemaatika teoreetilisi ja rakenduslikke küsimusi = Problems of pure and applied mathematics : konverentsi ettekannete teesid, 21-22.09.1990 (15−16).. Tartu: Tartu University Press.
2.5.
1989
Lõhmus, J.; Paal, E.; Sorgsepp, L. (1989). On currents and symmetries associated with Mal'tsev algebras. Tartu: Academy of Sciences of the Estonian S.S.R..
3.2.
1989
Paal, E. (1989). On bicombinatorial representation of the Moufang loops. И. Отс, В. Розенгаус. Фундаментальные поля (104−124).. Тарту : Академия наук Эстонской ССР. (Труды Института физики Академий наук Эстонской ССР ; 64).
5.2.
1989
Paal, E. (1989). On a Nonassociative Extension of Group Theoretical Method Based on Moufang Loops and Mal'tsev Algebras. Theory of Models and Algebras. Int. Con. on Algebra Dedicated to A. I. Mal'tsev, Novosibirsk, Aug. 21-26, 1989: Int. Con. on Algebra Dedicated to A. I. Mal'tsev, Novosibirsk, Aug. 21-26, 1989. Novisibirsk: Russian Academy of Sciences, 97.
6.7.
1989
Paal, E. (1989). On a Nonassociative Extension of Group Theoretical Method Based on Moufang Loops and Mal'tsev Algebras. (Doktoritöö, Eesti Teaduste Akadeemia). Eesti Teaduste Akadeemia.
6.7.
1989
Lõhmus, J.; Paal, E.; Sorgsepp, L. (1989). On Currents and Symmetries Associated with Mal'tsev Algebras. In: .. Tartu: Academy of Sciences of the Estonian S.S.R.. (Preprint / Academy of Sciences of the Estonian S.S.R., section of Physics and Astronomy; F-50).
2.5.
1988
Paal, E. (1988). Analytic Moufang-transformations. Tartu: Academy of Sciences of the Estonian S.S.R..
6.7.
1988
Paal, E. (1988). Analytic Moufang Transformations. In: .. Tartu: Academy of Sciences of the Estonian S.S.R.. (Preprint / Academy of Sciences of the Estonian S.S.R., Section of Physics and Astronomy; F-46).
2.5.
1987
Паал, Э. (1987). Введение в Муфанг-симметрию. . Тарту : Академия наук Эстонской ССР. (Препринт / Академия наук Эстонской ССР, отделение физики и астрономии; F-42).
3.2.
1987
Paal, E. (1987). Moufang transformations. П. Кууск и Я. Лыхмус. Фундаментальные взаимодействия (142−158).. Тарту : Академия Наук ЭССР. (Труды Института физики / Академия наук ЭССР; 62).
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ERMOSERMOS7Lie algebrate kohomoloogia, mitteassotsiatiivsed struktuurid, dünaamilised süsteemid ja operaadid.01.12.201030.11.2013Pasha ZusmanovichTallinna Tehnikaülikool, Matemaatika-loodusteaduskond92 671,89 EUR
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ETFETF5634Operaadid ja kohomoloogia01.01.200331.12.2006Eugen PaalTallinna Tehnikaülikool, Matemaatika-loodusteaduskond19 914,87 EUR
ETFETF9038Operaadid, deformatsioonid, dünaamika01.01.201231.12.2015Eugen PaalTallinna Tehnikaülikool, Matemaatika-loodusteaduskond45 312,00 EUR
ETFETF6912Üldistatud Lie Teooria01.01.200731.12.2010Eugen PaalTallinna Tehnikaülikool, Matemaatika-loodusteaduskond22 548,04 EUR