Integrable systems associated with generalized Sklyanin algebra

2008/12/28 by Yu. B. Chernyakov, Chernyakov, Yu.
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0812.4786

openalex publication_date 2008/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the point fusion procedure we obtain the new integrable systems from the Elliptic Schlesinger system (ESS). These new systems have the pole orders higher than one in the matrix of the Lax operator. Quadratic Poisson algebras on the phase space of the new systems generalize the Sklyanin algebras and have the graduated structure.

Related

• Elliptic Sklyanin integrable systems for arbitrary reductive groups
• Integrable Systems, Obtained by Point Fusion from Rational and Elliptic Gaudin Systems
• Polynomilal Poisson algebras with regular structure of symplectic leaves
• Integrable systems associated with elliptic algebras
• Commutative Poisson subalgebras for the Sklyanin bracket and deformations of known integrable models