Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Complete list of metadata

Cited literature [20 references]  Display  Hide  Download
Contributor : Vladimir Roubtsov <>
Submitted on : Tuesday, August 28, 2012 - 3:42:35 PM
Last modification on : Monday, March 9, 2020 - 6:15:56 PM
Long-term archiving on: : Thursday, November 29, 2012 - 3:36:28 AM


Files produced by the author(s)


  • HAL Id : hal-00725993, version 1


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



Record views


Files downloads