Russian Academy of Sciences

Landau Institute for Theoretical Physics

Aleksandr V. Odesskii

Senior researcher (associated) (associated)

Doctor of science

Email:

Publications

    1. Boris Feigin, Alexander Odesskii, Functional equations in algebra, arXiv:1709.00750, ADS: 2017arXiv170900750F.
    2. A. Odesskii, V. Rubtsov, V. Sokolov, Parameter-dependent associative Yang-Baxter equations and Poisson brackets, Int. J. Geom. Methods Mod. Phys. 11(9), 1460036 (2014) [18 pages]; arXiv:1311.4321, WoS: 000344230400013, Scopus: 2-s2.0-84908628170, ADS: 2014IJGMM..1160036O, RINTs: 23998016, MathSciNet: 3270299, zbMath: 1314.16024.
    3. V.E. Zakharov, A.V. Odesskii, M. Tsisternino, M. Onorato, Pyativolnovaya klassicheskaya matritsa rasseyaniya i integriruemye uravneniya, TMF, 180(1), 10-16 (2014) [V.E. Zakharov, A.V. Odesskii, M. Cisternino, M. Onorato, Five-wave classical scattering matrix and integrable equations, Theor. Math. Phys., 180(1), 759–764 (2014)], WoS: 000340457900002, Scopus: 2-s2.0-84905641883, ADS: 2014TMP...180..759Z, RINTs: 21826693, MathSciNet: 3344491, zbMath: 1308.76043, EDN: SJQMBX.
    4. A.V. Odesskii, V.V. Sokolov, Non-homogeneous systems of hydrodynamic type possessing Lax representations, Commun. Math. Phys., 324(1), 47-62 (2013); arXiv:1206.5230, WoS: 000325626900002, Scopus: 2-s2.0-84885579087, ADS: 2013CMaPh.324...47O, RINTs: 21881134, MathSciNet: 3116315, zbMath: 1282.37036.
    5. A. Odesskii, V. Rubtsov, V. Sokolov, Double Poisson brackets on free associative algebras, Contemp. Math., 592, 225-239 (2013) [Noncommutative Birational Geometry, Representations and Combinatorics, Ed. by A. and V. Retakh, AMS, 2013. ISBNs: 978-0-8218-8980-0 (print); 978-1-4704-0971-5 (online)]; arXiv:1208.2935, WoS: 000320089500010, MathSciNet: 3087947, zbMath: 1321.17014.
    6. V.E. Zakharov, A.V. Odesskii, M. Onorato, M. Cisternino, Integrable equations and classical S-matrix, arXiv:1204.2793, ADS: 2012arXiv1204.2793Z.
    7. E.V. Ferapontov, A.V. Odesskii, N.M. Stoilov, Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions, J. Math. Phys., 52, 073305 (2011) [28 pages]; arXiv:1007.3782, WoS: 000293478000020, Scopus: 2-s2.0-79960896709, ADS: 2011JMP....52g3505F, RINTs: 17115651, MathSciNet: 2849038, zbMath: 1317.37071.
    8. A. Odesskii, V. Sokolov, Classification of integrable hydrodynamic chains, J. Phys. A: Math. Theor. 43, 434027, 15 p. (2010); arXiv:1001.0020, WoS: 000283300100028, Scopus: 2-s2.0-78649662354, ADS: 2010JPhA...43Q4027O, RINTs: 16917222, MathSciNet: 2727801, zbMath: 1220.37056.
    9. E.V. Ferapontov, A.V. Odesskii, Integrable Lagrangians and modular forms, Journal of Geometry and Physics, 60(6-8), 896-906 (2010); arXiv:0707.3433, WoS: 000278394300005, Scopus: 2-s2.0-77952546178, ADS: 2010JGP....60..896F, RINTs: 15442070, MathSciNet: 2647291, zbMath: 1188.35161.
    10. A. Odesskii, V. Sokolov, Integrable pseudopotentials related to generalized hypergeometric functions, Selecta Math. New Ser., 16(1), 145-172 (2010); arXiv:0803.0086, WoS: 000276068500003, Scopus: 2-s2.0-77950020760, ADS: 2008arXiv0803.0086O, RINTs: 5335739, MathSciNet: 2609646, zbMath: 1274.37040.
    11. A.V. Odesskii, V.V. Sokolov, Integriruemye (2+1)-mernye sistemy gidrodinamicheskogo tipa, TMF, 163(2), 179–221 (2010) [A.V. Odesskii, V.V. Sokolov, Integrable (2+1)-dimensional systems of hydrodynamic type, Theor. Math. Phys., 163(2), 549-586 (2010)]; arXiv:1009.2778, WoS: 000278584200001, Scopus: 2-s2.0-77953508429, ADS: 2010TMP...163..549O, RINTs: 15334421, MathSciNet: -, zbMath: 1303.37024.
    12. A.V. Odesskii, V.V. Sokolov, Integriruemye ellipticheskie psevdopotentsialy, TMF, 161(1), 21-36 (2009) [A.V. Odesskii, V.V. Sokolov, Integrable elliptic pseudopotentials, Theoretical & Mathematical Physics, 161(1), 1340-1352 (2009)]; arXiv:0810.3879, WoS: 000271645400002, Scopus: -?, ADS: 2009TMP...161.1340O, RINTs: 20732086, MathSciNet: 2664881, zbMath: 1180.37096.
    13. A.V. Odesskii, V.V. Sokolov, Systems of Gibbons-Tsarev type and integrable 3-dimensional models, arXiv:0906.3509, ADS: 2009arXiv0906.3509O.
    14. A. Odesskii, V. Sokolov, Pairs of compatible associative algebras, classical Yang-Baxter equation and quiver representations, Commun. Math. Phys., 278 (1), 83-99 (2008); math/0611200, WoS: 000252191200003, Scopus: 2-s2.0-38049058447, ADS: 2008CMaPh.278...83O, RINTs: 13582273, MathSciNet: 2431852.
    15. A. Odesskii, A family of (2+1)-dimensional hydrodynamic type systems possessing a pseudopotential, Selecta Mathematica-New Series, 13(4), 727-742 (2008); arXiv:0704.3577, WoS: 000255680500006, Scopus: 2-s2.0-44249123985, ADS: 2007arXiv0704.3577O, InSpire: 750425, RINTs: 13542718, MathSciNet: 2403309, zbMath: 1237.37048.
    16. A.V. Odesskii, M.V. Pavlov, V.V. Sokolov, Klassifikatsiya integriruemykh uravnenii tipa uravneniya Vlasova, TMF, 154(2), 249-260 (2008) [A.V. Odesskii, M.V. Pavlov, V.V. Sokolov, Classification of integrable Vlasov-type equations, Theor. Math. Phys, 154(2), 209–219 (2008)]; arXiv:0710.5655, WoS: 000253216500004, Scopus: 2-s2.0-39349117644, ADS: 2008TMP...154..209O, RINTs: 13592339, MathSciNet: 2424005, zbMath: 1146.76061.
    17. A.V. Odesskii, V.V. Sokolov, O (2+1)-mernykh sistemakh gidrodinamicheskogo tipa, obladayushchikh psevdopotentsialom s podvizhnymi osobennostyami, Funkts. analiz i ego pril., 42(3), 53-62 (2008) [A.V. Odesskii, V.V. Sokolov, On (2+1)-dimensional hydrodynamic type systems possessing a pseudopotential with movable singularities, Func. Anal. and Its Appl, 42(3), 205-212 (2008)]; math-ph/0702026, WoS: 000259070800005, Scopus: 2-s2.0-39349096241, ADS: 2007math.ph...2026O, InSpire: 744281, RINTs: 20730512, MathSciNet: 2454476, zbMath: 1175.35028.
    18. A. Odesskii, V. Rubtsov, 2432990, Quantum Groups, 12, European Mathematical Society, pp. 81-105, 2008 [IRMA Lectures in Mathematics and Theoretical Physics, Vol. 12, 9, pp. 81-105, 2008. ISBN: 78-3-03-719047-0.]; math/0404159, WoS: 000267347700004, Scopus: -, ADS: 2004math......4159O, RINTs: -, MathSciNet: 2432990, zbMath: 1202.81099.
    19. A. Odesskii, V. Sokolov, Algebraic structures connected with pairs of compatible associative algebras, Int. Math. Res. Notices, 2006, 43734 (2006); math/0512499, WoS: 000242575800001, Scopus: 2-s2.0-33751543975, ADS: 2005math.....12499O, InSpire: 701339, RINTs: 13522385, MathSciNet: 2264716, zbMath: 1151.16030.
    20. A.V. Odesskii, V.V. Sokolov, Compatible Lie brackets related to elliptic curve, J. Math. Phys., 47, 013506 (2006); math/0506503, WoS: 000235015000024, Scopus: 2-s2.0-31644441801, ADS: 2006JMP....47a3506O, InSpire: 686062, RINTs: 13518522, MathSciNet: 2201803.
    21. A.V. Odesskii, V.V. Sokolov, Integrable matrix equations related to pairs of compatible associative algebras, J. Phys. A 39(40), 12447-12456 (2006); math/0604574, WoS: 000241543300014, Scopus: 2-s2.0-33748983548, ADS: 2006JPhA...39..011O, InSpire: 715468, RINTs: 13517660, MathSciNet: 2265833, zbMath: 1151.16030.
    22. A.V. Odesskii, BiHamiltonian elliptic structures, Moscow Math. J., 4(4), 941-946 (2004); math/0212210, WoS: 000208595000007, Scopus: -, ADS: 2002math.....12210O, InSpire: 604850, MathSciNet: 2124173, zbMath: 1065.14043.
    23. A. Odesskii, V. Rubtsov, Integrable systems associated with elliptic algebras, Rokko Lectures in Mathematics (18. Elliptic Integrable Systems), 111-132, 2005 [The proceedings of Workshop on Elliptic Integrable Systems, November 8-11, 2004, Kyoto, pp. 111-132]; math/0404159, ADS: 2004math......4159O.
    24. A. Odesskii, Set-theoretical solutions to the Yang-Baxter relation from factorization of matrix polynomials and θ-functions, Moscow Math. J., 3(1), 97-103 (2003); math/0205051, WoS: 000208594100008, Scopus: -, ADS: 2002math......5051O, RINTs: 8379149, MathSciNet: 1996805, zbMath: 1052.81050.
    25. B. Enriquez, A. Odesskii, Quantization of canonical cones of algebraic curves, Ann. Inst. Fourier, 52 (6), 1629-1663 (2002); math/0112148, WoS: 000181391300002, Scopus: 2-s2.0-0038168024, ADS: 2001math.....12148E, RINTs: 13416396, MathSciNet: 1952526, zbMath: 1052.14035.
    26. H.W. Braden, A. Gorsky, A. Odesskii, V. Rubtsov, Double-elliptic dynamical systems from generalized Mukai-Sklyanin algebras, Nucl. Phys. B 633 (3), 414-442 (2002); hep-th/0111066, WoS: 000176318500005, Scopus: 2-s2.0-0036606583, ADS: 2002NuPhB.633..414B, InSpire: 565869, RINTs: 13394087, MathSciNet: 1910270, zbMath: 0995.37044.
    27. A.A. Belavin, A.V. Odesskii, R.A. Usmanov, Novye sootnosheniya v algebre Q-operatorov Bakstera, TMF, 130(3), 383-413 (2002) [A.A. Belavin, A.V. Odesskii, R.A. Usmanov, New relations in the algebra of the Baxter Q-operators, Theor. Math. Phys., 130(3), 323-350 (2002)]; hep-th/0110126, WoS: 000175360600002, Scopus: 2-s2.0-0036248328, ADS: 2001hep.th...10126B, InSpire: 564359, RINTs: 13392121, MathSciNet: 1920471, zbMath: 1044.81130, EDN: LHBOHT.
    28. A.V. Odesskii, V.N. Rubtsov, Polinomial’nye algebry Puassona s regulyarnoi strukturoi simplekticheskikh listov, TMF, 133(1), 3-23 (2002) [A.V. Odesskii, V.N. Rubtsov, Polynomilal Poisson algebras with regular structure of symplectic leaves, Theoret. Math. Phys., 133(1), 1321-1337 (2002)]; math/0110032, WoS: 000179367800001, Scopus: 2-s2.0-0036407126, ADS: 2001math.....10032O, RINTs: 13397128, MathSciNet: 1992166, zbMath: 1138.53314.
    29. A.V. Odesskii, Ellipticheskie algebry, Uspekhi mat. nauk, 57:6(348), 87–122 (2002) [A.V. Odesskii, Elliptic algebras, Russ. Math. Surv., 57(6), 1127-1162 (2002)]; math/0303021, WoS: 000182349100002, Scopus: 2-s2.0-0037988851, ADS: 2002RuMaS..57R...2O, RINTs: 14406747, MathSciNet: 1991863.
    30. A.V. Odesskii, Ellipticheskie R-matritsy Belavina i obmennye algebry, Funkts. analiz i ego pril., 36(1), 59-74 (2002) [A.V. Odesskii, Belavin elliptic R-matrices and exchange algebras, Funct. Anal. Appl., 36(1), 49-61 (2002)]; math/0211106, WoS: 000174777000005, Scopus: 2-s2.0-0036256656, ADS: 2002math.....11106O, InSpire: 601632, RINTs: 5025009, MathSciNet: 1898983, zbMath: 1022.17023.
    31. B.L. Feigin, A.V. Odesskii, Functional realization of some elliptic Hamiltonian structures and bosonization of the corresponding quantum algebras, NATO Science Series, Ser. II: Math. Phys. Chem. 35, 109-122 (2001) [Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory. Proceedings of the NATO Advanced Research Workshop on Dynamical Symmetries of Integrable Quantum Field Theories and Lattice Models, Kiev, Ukraine, September 25-30, 2000. Ed. by S. Pakuliak, G. von Gehlen. Dordrecht: Kluwer Academic Publishers, 2001, vii+335 pp. ISBN 0-7923-7183-6]; math/9912037, WoS: 000174167000007, ADS: 1999math.....12037O, MathSciNet: 1873567.
    32. B.L. Feigin, A.V. Odesskii, Quantized moduli spaces of the bundles on the elliptic curve and their applications, NATO Science Series, Ser. II: Math. Phys. Chem. 35, 123-137 (2001) [Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory. Proceedings of the NATO Advanced Research workshop on dynamical symmetries of integrable quantum field theory and lattice models, Kiev, Ukraine, September 25-30, 2000. Ed. by S. Pakuliak, G. von Gehlen. Dordrecht: Kluwer Academic Publishers, 2001, vii+335 pp. ISBN 0-7923-7183-6]; math/9812059, WoS: 000174167000008, ADS: 1998math.....12059O, MathSciNet: 1873568.
    33. A. Odesskii, Local action of the symmetric group and the twisted Yang-Baxter relation, math/0110268, ADS: 2001math.....10268O, InSpire: 565200.
    34. B. Feigin, M. Jimbo, T. Miwa, A. Odesskii, Ya. Pugai, Algebra of screening operators for the deformed Wn algebra, Commun. Math. Phys., 191 (3), 501-541 (1998); q-alg/9702029, WoS: 000072325700002, Scopus: 2-s2.0-0032472514, ADS: 1998CMaPh.191..501F, InSpire: 441264, MathSciNet: 1608555, zbMath: 0952.17010.
    35. B.L. Feĭgin, A.V. Odesskiĭ, Coordinate ring of the quantum Grassmannian and intertwiners for the representations of Sklyanin algebras, Amer. Math. Soc. Transl. Ser. 2, Vol. 185(38), 55-64 (1998) [Topics in Quantum Groups and Finite-Type Invariants: Mathematics at the Independent University of Moscow, B. Feigin and V. Vassiliev, Editors, AMS, 1998, 182 pp.; ISBN-10: 0-8218-1084-7, ISBN-13: 978-0-8218-1084-2], MathSciNet: 1736163, zbMath: 0923.16028.
    36. B.L. Feĭgin, A.V. Odesskiĭ, Vector bundles on an elliptic curve and Sklyanin algebras, Amer. Math. Soc. Transl. Ser. 2, Vol. 185(38), 65-84 (1998) [Topics in Quantum Groups and Finite-Type Invariants: Mathematics at the Independent University of Moscow, B. Feigin and V. Vassiliev, Editors, AMS, 1998, 182 pp.; ISBN-10: 0-8218-1084-7, ISBN-13: 978-0-8218-1084-2], MathSciNet: 1736164, zbMath: 0916.16014.
    37. A.V. Odesskii, B.L. Feigin, Quantized moduli spaces of the bundles on the elliptic curve and their applications, math/9812059, ADS: 1998math.....12059O.
    38. B. Feigin, A. Odesskii, A family of elliptic algebras, Int. Math. Res. Notices, 1997(11), 531-539 (1997), WoS: A1997XN22700003, Scopus: 2-s2.0-0038764719, ADS: -, RINTs: 24728719, MathSciNet: 1448336, zbMath: 0923.16027.
    39. A.V. Odesskii, B.L. Feigin, Ellipticheskie deformatsii algebr tokov i ikh predstavleniya raznostnymi operatorami, Funkts. analiz i ego pril., 31(3), 57-70 (1997) [A.V. Odesskii, B.L. Feigin, Elliptic deformations of current algebras and their representations by difference operators, Funct. Anal. Appl., 31(3), 193-203 (1997)], WoS: 000073662400006, Scopus: 2-s2.0-27244433380, ADS: -, MathSciNet: 1479076, zbMath: 0919.17009.
    40. A.V. Odesskii, B.L. Feigin, Ellipticheskie algebry Sklyanina. Sluchai tochki konechnogo poryadka, Funkts. analiz i ego pril., 29(2), 9–21 (1995) [A.V. Odesskii, B.L. Feigin, Elliptic Sklyanin algebras. The case of points of finite order, Funct. Anal. Appl., 29(2), 81-90 (1995)], WoS: A1995TH47600002, Scopus: 2-s2.0-34249757721.
    41. B.L. Feigin, A.V. Odesskii, Vector bundles on elliptic curve and Sklyanin algebras, Preprint RIMS-1032, Sep 1995. 26pp; q-alg/9509021, ADS: 995q.alg.....9021F.
    42. A.V. Odessky, B.L. Feigin, Sklyanin elliptic algebras. The Case of points of finite order, Preprint RIMS-986, Jul 1994. 15pp.
    43. A.V. Odesskii, B.L. Feigin, Konstruktsii ellipticheskikh algebr Sklyanina i kvantovykh R-matrits, Funkts. analiz i ego pril., 27(1), 37–45 (1993) [A.V. Odesskii, B.L. Feigin, Constructions of Sklyanin elliptic algebras and quantum R-Matrices, Funct. Anal. Appl., 27(1), 31–38 (1993)], WoS: A1993LQ87700005, Scopus: 2-s2.0-34249764695, MathSciNet: 1225909.
    44. A.V. Odesskii, B.L. Feigin, Ellipticheskie algebry Sklyanina, Funkts. analiz i ego pril., 23(3), 45–54 (1989) [A.V. Odesskii, B.L. Feigin, Sklyanin elliptic algebras, Funct. Anal. Appl., 23(3), 207–214 (1989)].
    45. A.V. Odesskii, Ob odnom analoge algebry Sklyanina, Funkts. analiz i ego pril., 20(2), 78–79 (1986) [A.V. Odesskii, An analog of the Sklyanin algebra, Funct. Anal. Appl., 20(2), 152–154 (1986)].