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