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Double Poisson brackets on free associative algebras

Abstract : We discuss double Poisson structures in sense of M. Van den Bergh on free associative algebras focusing on the case of quadratic Poisson brackets. We establish their relations with an associative version of Young-Baxter equations, we study a bi-hamiltonian property of the linear-quadratic pencil of the double Poisson structure and propose a classification of the quadratic double Poisson brackets in the case of the algebra with two free generators. Many new examples of quadratic double Poisson brackets are proposed.
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https://hal.archives-ouvertes.fr/hal-00725993
Contributor : Vladimir Roubtsov Connect in order to contact the contributor
Submitted on : Tuesday, August 28, 2012 - 3:42:35 PM
Last modification on : Wednesday, October 20, 2021 - 3:18:45 AM
Long-term archiving on: : Thursday, November 29, 2012 - 3:36:28 AM

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  • HAL Id : hal-00725993, version 1

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Alexander Odesskii, Vladimir Rubtsov, Vladimir Sokolov. Double Poisson brackets on free associative algebras. 2012. ⟨hal-00725993⟩

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