SHARCNET Research Chair and Associate Professor of Mathematics
My main research interests are in Mathematical Physics in the sense of Mathematics inspired by ideas that come from Theoretical Physics. More precisely, I am interested in algebraic and geometric structures which come from quantum field theory, statistical mechanics and the theory of integrable systems.
Academic Journal Papers, refereed
- Odesskii A. V., Feigin B. L., Elliptic deformations of current algebras and their representations by difference operators (Russian) Funktsional. Anal. i Prilozhen. 31 (1997), no. 3, 5770, 96; translation in Funct. Anal. Appl. 31 (1997), no. 3, 193203 (1998) (Reviewer: V. Leksin).
- Feigin Boris, Jimbo Michio, Miwa Tetsuji, Odesskii Alexander, Pugai Yaroslav, Algebra of screening operators for the deformed Walgebra. Comm. Math. Phys. 191 (1998), no. 3, 501541 . (Reviewer: Junichi Shiraishi), Full text
- Feigin Boris, Odesskii Alexander, A family of elliptic algebras. Internat. Math. Res. Notices 1997, no. 11, 531539. (Reviewer: Michel Van den Bergh).
- Odesskii A. V., Feigin B. L., Sklyanin’s elliptic algebras. The case of a point of finite order. (Russian) Funktsional. Anal. i Prilozhen. 29 (1995), no. 2, 921, 95; translation in Funct. Anal. Appl. 29 (1995), no.2, 8190.
- Odesskii A. V., Feigin B. L., Constructions of elliptic Sklyanin algebras and of quantum Rmatrices. (Russian) Funktsional. Anal. i Prilozhen. 27 (1993), no. 1, 3745; translation in Functional Anal. Appl. 27(1993), no. 1, 3138 (Reviewer: Tomasz Brzezinski).
- Odesski A. V., Rational degeneration of elliptic quadratic algebras. Infinite analysis, Part A, B ( Kyoto , 1991), 773779, Adv. Ser. Math. Phys., 16, World Sci. Publishing, River Edge, NJ, 1992. (Reviewer: Michel Van den Bergh)
- Odesskii A. V., Feigin B. L., Sklyanin’s elliptic algebras. (Russian) Funktsional. Anal. i Prilozhen. 23 (1989), no. 3, 4554, 96; translation in Functional Anal. Appl. 23 (1989), no. 3, 207214 (1990) (Reviewer: S.Paul Smith).
- Odesskii A. V., An analogue of the Sklyanin algebra. (Russian) Funktsional. Anal. i Prilozhen. 20 (1986), no. 2, 7879.
- A.V.Odesskii and B.L.Feigin, Coordinate ring of the quantum grassmanian and intertwiners for the representations of Sklyanin algebras. Topics in quantum groups and finitetype invariants, 5564, Amer. Math. Soc. Transl. Ser. 2, 185, Amer. Math. Soc., Providence , RI , 1998. (Reviewer: Michel Van den Bergh),
- B.L.Feigin and A.V.Odesskii, Vector bundles on elliptic curve and Sklyanin algebras. Topics in quantum groups and finitetype invariants, 6584, Amer. Math. Soc. Transl. Ser. 2, 185, Amer. Math. Soc., Providence , RI , 1998. (Reviewer: Michel Van den Bergh), qalg/9509021
- A.Odesskii and V.Rubtsov, Polynomial Poisson algebras with regular structure of symplectic leaves. Theoretical and Mathematical Physics V.133, no.1 (2002),
- A.Odesskii, Belavin Elliptic Rmatrices and exchange algebras. (Russian) Funktsional. Anal. i Prilozhen. 36 (2002), no. 1, 5974, 96; translation in Funct. Anal. Appl. 36 (2002), no. 1, 4961,
- A.Belavin, A.Odesskii and R.Usmanov, New relations in the algebra of the Baxter Qoperators. Theoretical and Mathematical Physics V.130, no.3 (2002), 383413,
- A.Odesskii, Set-theoretical solutions to the YangBaxter Relation from factorization of matrix polynomials and thetafunctions. Mosc. Math. J. 3 (2003), no. 1, 97103, math.QA/0205051
- B.Enriquez, A.Odesskii, Quantization of canonical cones of algebraic curves. Ann. Inst. Fourier ( Grenoble ) 52 (2002), no. 6, 16291663, math.AG/0112148
- H. Braden, A. Gorsky, A. Odesskii, V. Rubtsov, Double Elliptic Dynamical Systems From Generalized Mukai Sklyanin Algebras. Nuclear Phys. B 633 (2002), no. 3, 414442, Full text
- A.Odesskii, Bihamiltonian elliptic structures. Mosc. Math. J. 4 (2004), no. 4, 941—946, math.QA/0212210
- A.Odesskii, V. Sokolov, Compatible Lie brackets related to elliptic curve. Journal of Mathematical Physics 47, 013506 (2006),
- A.Odesskii, V.Sokolov, Integrable matrix equations related to pairs of compatible associative algebras. J. Phys. A: Math. Gen. 39 (2006), 1244712456,
- A.Odesskii, V.Sokolov, Algebraic structures connected with pair of compatible associative algebras. International Mathematical Research Notices, vol. 2006, Article ID 43734, 35 pages, 2006,
- A.Odesskii, V.Sokolov, Pairs of compatible associative algebras, classical YangBaxter equation and quiver representations. Communications in Mathematical Physics, vol. 278, 1 (2008), 8399, math.QA/0611200
- A.Odesskii, V.Sokolov, On (2+1)D hydrodynamic type systems possessing pseudopotential with movable singularities, Functional. Anal. Appl. V.42, no. 3, July 2008, mathph/0702026
- A.Odesskii, A family of (2+1)dimensional hydrodynamictype systems possessing a pseudopotential. Selecta Math. (N.S.) 13 (2008), no. 4, 727—742, arXiv:0704.3577
- A.Odesskiĭ, M.Pavlov, V.Sokolov, Classification of integrable Vlasovtype equations. (Russian) Teoret. Mat. Fiz. 154 (2008), no. 2, 249—260, arXiv:0710.5655
Review Articles, refereed
- A.Odesskii, Elliptic algebras. Russian Mathematical Surveys V.57 (2002) no. 6, Full text
Conference contributions, refereed
- A.V.Odesskii and B.L.Feigin, Quantized moduli spaces of the bundles on the elliptic curve and their applications. Integrable structures of exactly solvable twodimensional models of quantum field theory ( Kiev , 2000), 123137, NATO Sci. Ser. II Math. Phys. Chem., 35, Kluwer Acad. Publ., Dordrecht , 2001. (Reviewer: Zhenbo Qin), math.QA/9812059
- A.V.Odesskii and B.L.Feigin, Functional realization of some elliptic Hamiltonia structures and bosonization of the corresponding quantum algebras. Integrable structures of exactly solvable twodimensional models of quantum field theory ( Kiev , 2000), 109122, NATO Sci. Ser. II Math. Phys. Chem., 35, Kluwer Acad. Publ., Dordrecht , 2001. (Reviewer: ShaoMing Fei), math.QA/9912037
- A. Odesskii, V. Rubtsov, Integrable systems associated with elliptic algebras. The proceedings of the Workshop on Elliptic Integrable Systems, Rokko Lectures in Mathematics, N 18, Eds. M. Noumi and K. Takasaki, math.QA/0404159 Preprints • E. V. Ferapontov, A. V. Odesskii, Integrable Lagrangians and modular forms, arXiv:0707.3433
Preprints
- E. V. Ferapontov, A. V. Odesskii, Integrable Lagrangians and modular forms, arXiv:0707.3433
- A.Odesskii, V.Sokolov, Integrable pseudopotentials related to generalized hypergeometric functions, arXiv:0803.0086
- A.Odesskii, V.Sokolov, Integrable pseudopotentials related to elliptic curves, arXiv:0810.3879
- MATH 3P09 Partial Differential Equations
- MATH 2P08 Ordinary Differential Equations
- MATH 3P08 Advanced Differential Equations