1 citations · 1 across the 5 of their papers we have counts for
8 papers
Integrable systems associated with elliptic algebras
A. Odesskii, V. Rubtsov
We construct some new Integrable Systems (IS) both classical and quantum associated with elliptic algebras. Our constructions are partly based on the algebraic integrability mechan…
Elliptic algebras
Alexander Odesskii
The survey is devoted to associative -graded algebras presented by n generators and n(n-1)/2 quadratic relations and satisfying the so-called Poincare-Birkhoff-Witt cond…
Bihamiltonian elliptic structures
Alexander Odesskii
We construct three compatible quadratic Poisson structures such that generic linear combination of them is associated with Elliptic Sklyanin algebra in n generators. Symplectic lea…
Belavin Elliptic R-Matrices and Exchange Algebras
Alexander Odesskii
We study Zamolodchikov algebras whose commutation relations are described by Belavin matrices defining a solution of the Yang-Baxter equation (Belavin -matrices). Homomorphisms…
Set-theoretical solutions to the Yang-Baxter Relation from factorization of matrix polynomials and -functions
Alexander Odesskii
New set-theoretical solutions to the Yang-Baxter Relation are constructed. These solutions arise from the decompositions "in different order" of matrix polynomials and -function…
Local action of the symmetric group and the twisted Yang-Baxter relation
Alexander Odesskii
The generalization of the the Yang-Baxter relation is proposed. In this generalization the spectral parameters of the particles change after the scattering. The corresponding algeb…