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Double Poisson algebras

Michel Van den Bergh
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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.

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Michel Van den Bergh. 2007-03-02. Double Poisson algebras. https://arxiv.org/abs/math/0410528

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