Russian Academy of Sciences

Landau Institute for Theoretical Physics

Aleksandr V. Odesskii

Senior researcher (associated)

Doctor of science

Email:

Publications

    1. Boris Feigin, Alexander Odesskii, Functional equations in algebra, arXiv:1709.00750.
    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.
    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.
    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.
    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.
    6. V.E. Zakharov, A.V. Odesskii, M. Onorato, M. Cisternino, Integrable equations and classical S-matrix, arXiv:1204.2793.
    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.
    8. A. Odesskii, V. Sokolov, Classification of integrable hydrodynamic chains, J. Phys. A: Math. Theor. 43, 434027, 15 p. (2010); arXiv:1001.0020, Scopus: 2-s2.0-78649662354.
    9. A. Odesskii, V. Sokolov, Integrable pseudopotentials related to generalized hypergeometric functions, Sel. Math. New Ser., 16(1), 145-172 (2010); arXiv:0803.0086, Scopus: 2-s2.0-77950020760.
    10. 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, Scopus: 2-s2.0-77953508429.
    11. A.V. Odesskii, V.V. Sokolov, Integriruemye ellipticheskie psevdopotentsialy, TMF, 161(1), 21–36 (2009) [A.V. Odesskii, V.V. Sokolov, Integrable elliptic pseudopotentials, Theor. Math. Phys., 161(1), 1340–1352 (2009)]; arXiv:0810.3879.
    12. A.V. Odesskii, V.V. Sokolov, Systems of Gibbons-Tsarev type and integrable 3-dimensional models, arXiv:0906.3509.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. A. Odesskii, V. Sokolov, Integrable pseudopotentials related to elliptic curves, arXiv:0810.3879.
    18. E.V. Ferapontov, A.V. Odesskii, Integrable Lagrangians and modular forms, arXiv:0707.3433.
    19. A. Odesskii, V. Sokolov, Algebraic structures connected with pairs of compatible associative algebras, Int. Math. Res. Notices, 2006, 43734 (2006); math/0512499.
    20. A.V. Odesskii, V.V. Sokolov, Compatible Lie brackets related to elliptic curve, J. Math. Phys., 47, 013506 (2006); math/0506503.
    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.
    22. A.V. Odesskii, Bihamiltonian elliptic structures, Moscow Math. J., 4(4), 941-946 (2004); math/0212210.
    23. A. Odesskii, V. Rubtsov, Integrable systems associated with elliptic algebras, math/0404159.
    24. A. Odesskii, Set-theoretical solutions to the Yang-Baxter relation from factorization of matrix polynomials and $\theta$-functions, Moscow Math. J., 3(1), 97-103 (2003); math/0205051.
    25. B. Enriquez, A. Odesskii, Quantization of canonical cones of algebraic curves, Ann. Inst. Fourier, 52 (6), 1629-1663 (2002); math/0112148.
    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.
    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.
    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, Polynomial Poisson algebras with regular structure of symplectic leaves, Theor. Math. Phys., 133(1), 1321–1337 (2002)].
    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.
    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.
    31. B.L. Feigin, A.V. Odesskii, Functional realization of some elliptic Hamiltonian structures and bosonization of the corresponding quantum algebras, NATO Sci. 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 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/9912037.
    32. B.L. Feigin, A.V. Odesskii, Quantized moduli spaces of the bundles on the elliptic curve and their applications, NATO Sci. 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.
    33. A. Odesskii, V. Rubtsov, Polynomilal Poisson algebras with regular structure of symplectic leaves, math/0110032.
    34. A. Odesskii, Local action of the symmetric group and the twisted Yang-Baxter relation, math/0110268.
    35. 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.
    36. 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].
    37. 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].
    38. A.V. Odesskii, B.L. Feigin, Quantized moduli spaces of the bundles on the elliptic curve and their applications, math/9812059.
    39. B. Feigin, A. Odesskii, A family of elliptic algebras, Int. Math. Res. Notices, 1997(11), 531-539 (1997).
    40. 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)].
    41. 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)].
    42. B.L. Feigin, A.V. Odesskii, Vector bundles on elliptic curve and Sklyanin algebras, Preprint RIMS-1032, Sep 1995. 26pp; q-alg/9509021.
    43. A.V. Odessky, B.L. Feigin, Sklyanin elliptic algebras. The Case of points of finite order, Preprint RIMS-986, Jul 1994. 15pp.
    44. 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)].
    45. 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)].
    46. 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)].