Parameter-dependent associative Yang-Baxter equations and Poisson brackets

摘要

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