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Parameter-dependent associative Yang-Baxter equations and Poisson brackets

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.

Dates and versions

hal-00931983 , version 1 (16-01-2014)

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Alexander Odesskii, Vladimir Rubtsov, Vladimir Sokolov. Parameter-dependent associative Yang-Baxter equations and Poisson brackets. 2013. ⟨hal-00931983⟩
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