English

Parameter-dependent associative Yang-Baxter equations and Poisson brackets

Mathematical Physics 2015-06-17 v2 math.MP

Abstract

We discuss associative analogues of classical Yang-Baxter equation meromorphically dependent on parameters. We discover that such equations enter in a description of a general class of parameter-dependent Poisson structures and double Lie and Poisson structures in sense of M. Van den Bergh. We propose a classification of all solutions for one-dimensional associative Yang-Baxter equations.

Keywords

Cite

@article{arxiv.1311.4321,
  title  = {Parameter-dependent associative Yang-Baxter equations and Poisson brackets},
  author = {Alexander Odesskii and Vladimir Rubtsov and Vladimir Sokolov},
  journal= {arXiv preprint arXiv:1311.4321},
  year   = {2015}
}

Comments

18 pages, LATEX2, ws-ijgmmp style. Few typos corrected, aknowledgements added

R2 v1 2026-06-22T02:09:24.974Z