Double Poisson brackets on free associative algebras
Exactly Solvable and Integrable Systems
2012-08-15 v1 Quantum Algebra
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.
Cite
@article{arxiv.1208.2935,
title = {Double Poisson brackets on free associative algebras},
author = {A. Odesskii and V. Rubtsov and V. Sokolov},
journal= {arXiv preprint arXiv:1208.2935},
year = {2012}
}
Comments
19 pages, latex