Trigonometric Integrable Tops from Solutions of Associative Yang–Baxter Equation

[1]  A. Zotov,et al.  R-matrix-valued Lax pairs and long-range spin chains , 2018, Physics Letters B.

[2]  A. Zotov,et al.  On R-matrix valued Lax pairs for Calogero–Moser models , 2017, Journal of Physics A: Mathematical and Theoretical.

[3]  M. Batchelor,et al.  Exactly solved models and beyond: a special issue in honour of R J Baxter’s 75th birthday , 2016, 1608.04899.

[4]  A. Zotov,et al.  Noncommutative extensions of elliptic integrable Euler–Arnold tops and Painlevé VI equation , 2016, 1603.06101.

[5]  Arun Ram Quantization of Lie groups and Lie algebras , 2016 .

[6]  Andrei Vladimirovich Zotov,et al.  Yang–Baxter equations with two Planck constants , 2015, Journal of Physics A: Mathematical and Theoretical.

[7]  Andrei Vladimirovich Zotov,et al.  Quantum Baxter-Belavin R-matrices and multidimensional lax pairs for Painlevé VI , 2015, 1501.07351.

[8]  Andrei Vladimirovich Zotov,et al.  Planck constant as spectral parameter in integrable systems and KZB equations , 2014, 1408.6246.

[9]  Andrei Vladimirovich Zotov,et al.  Classical integrable systems and soliton equations related to eleven-vertex R-matrix , 2014, 1406.2995.

[10]  Andrei Vladimirovich Zotov,et al.  Relativistic classical integrable tops and quantum R-matrices , 2014, 1405.7523.

[11]  A. Zotov,et al.  Rational top and its classical r-matrix , 2014, 1402.3189.

[12]  M. McCall,et al.  Rigid Body Dynamics , 2008 .

[13]  A. Smirnov Degenerate Sklyanin algebras , 2009, 0903.1466.

[14]  A. Polishchuk Massey products on cycles of projective lines and trigonometric solutions of the Yang-Baxter equations , 2006, math/0612761.

[15]  Andrei Vladimirovich Zotov,et al.  Квадратичные алгебры, связанные с эллиптическими кривыми@@@Quadratic algebras related to elliptic curves , 2008 .

[16]  Andrei Vladimirovich Zotov,et al.  Quadratic algebras related to elliptic curves , 2007 .

[17]  B. Kreußler,et al.  Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations , 2007, 0708.1685.

[18]  B. Khesin,et al.  Bihamiltonian Structures and Quadratic Algebras in Hydrodynamics and on Non-Commutative Torus , 2004 .

[19]  Andrei Vladimirovich Zotov,et al.  Hitchin Systems – Symplectic Hecke Correspondence and Two-Dimensional Version , 2001, Communications in Mathematical Physics.

[20]  T. Schedler Trigonometric solutions of the associative Yang-Baxter equation , 2002, math/0212258.

[21]  A. Polishchuk Classical Yang–Baxter Equation and the A∞-Constraint , 2002 .

[22]  Sergey Fomin,et al.  Quadratic Algebras, Dunkl Elements, and Schubert Calculus , 1999 .

[23]  A. Perelomov Quantum integrable systems and Clebsch-Gordan series: II , 1998 .

[24]  K.Hasegawa,et al.  On trigonometric intertwining vectors and non-dynamical R-matrix for the Ruijsenaars model , 1997, hep-th/9704074.

[25]  J. Avan,et al.  The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems , 1995, hep-th/9505091.

[26]  Nicolai Reshetikhin,et al.  Quantum Groups , 1993 .

[27]  J. Gervais,et al.  The quantum group structure associated with non-linearly extended Virasoro algebras , 1990 .

[28]  S. Ruijsenaars Complete integrability of relativistic Calogero-Moser systems and elliptic function identities , 1987 .

[29]  S. Ruijsenaars,et al.  A new class of integrable systems and its relation to solitons , 1986 .

[30]  Evgeny Sklyanin,et al.  Solutions of the Yang-Baxter equation , 1982 .

[31]  A. A. Belavin,et al.  Solutions of the classical Yang - Baxter equation for simple Lie algebras , 1982 .

[32]  E. Sklyanin Some algebraic structures connected with the Yang—Baxter equation , 1982 .

[33]  J. Perk,et al.  New families of commuting transfer matrices in q state vertex models , 1981 .

[34]  I. Cherednik On a method of constructing factorized S matrices in elementary functions , 1980 .

[35]  S. Manakov,et al.  Note on the integration of Euler's equations of the dynamics of an n-dimensional rigid body , 1976 .

[36]  L. Dikii Hamiltonian systems connected with the rotation group , 1972 .

[37]  Francesco Calogero,et al.  Solution of the One‐Dimensional N‐Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials , 1971 .

[38]  B. Sutherland Exact results for a quantum many body problem in one-dimension , 1971 .

[39]  A. Mishchenko Integral geodesics of A flow on Lie groups , 1970 .

[40]  F. Calogero Solution of a three-body problem in one-dimension , 1969 .

[41]  V. Arnold Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits , 1966 .