Double Poisson algebras
Quantum Algebra
2007-05-23 v4 Rings and Algebras
Abstract
In this paper we develop Poisson geometry for non-commutative algebras. This generalizes the bi-symplectic geometry which was recently, and independently, introduced by Crawley-Boevey, Etingof and Ginzburg. Our (quasi-)Poisson brackets induce classical (quasi-)Poisson brackets on representation spaces. As an application we show that the moduli spaces of representations associated to the deformed multiplicative preprojective algebras recently introduced by Crawley-Boevey and Shaw carry a natural Poisson structure.
Cite
@article{arxiv.math/0410528,
title = {Double Poisson algebras},
author = {Michel Van den Bergh},
journal= {arXiv preprint arXiv:math/0410528},
year = {2007}
}
Comments
Many misprints and inaccuracies (found by the referee) were corrected