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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.
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https://hal.archives-ouvertes.fr/hal-00931983
Contributor : Vladimir Roubtsov <>
Submitted on : Thursday, January 16, 2014 - 10:37:01 AM
Last modification on : Monday, March 9, 2020 - 6:15:58 PM

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  • HAL Id : hal-00931983, version 1
  • ARXIV : 1311.4321

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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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