Bihamiltonian elliptic structures

2002/12/16 by Alexander Odesskii, Odesskii, Alexander
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #hep-th #math.QA #nlin.SI

paper · pdf · doi:10.48550/arxiv.math/0212210

AMStex, 8 pages, minor changes

openalex publication_date 2002/12/16 · arxiv created 2003/01/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct three compatible quadratic Poisson structures such that generic linear combination of them is associated with Elliptic Sklyanin algebra in n generators. Symplectic leaves of this elliptic Poisson structure is studied. Explicit formulas for Casimir elements are obtained.

Related

• Polynomilal Poisson algebras with regular structure of symplectic leaves
• Quadratic algebras related to elliptic curves
• Poisson geometry and representations of PI 4-dimensional Sklyanin\n algebras
• Elliptic bihamiltonian structures from relative shifted Poisson structures
• Integrable systems associated with generalized Sklyanin algebra