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arXiv · 1311.4321

Parameter-dependent associative Yang-Baxter equations and Poisson brackets

Alexander Odesskii·Vladimir Rubtsov·Vladimir Sokolov
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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.

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Alexander Odesskii, Vladimir Rubtsov, Vladimir Sokolov. 2013-12-23. Parameter-dependent associative Yang-Baxter equations and Poisson brackets. https://doi.org/10.1142/s0219887814600366

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