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.
CITATION STYLE
Van den Bergh, M. (2008). Double Poisson algebras. Transactions of the American Mathematical Society, 360(11), 5711–5769. https://doi.org/10.1090/s0002-9947-08-04518-2
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