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arxiv: math/0410528 · v4 · submitted 2004-10-25 · 🧮 math.QA · math.RA

Double Poisson algebras

Michel Van den Bergh This is my paper
classification 🧮 math.QA math.RA
keywords poissonalgebrasbracketscrawley-boeveygeometryintroducedquasi-recently
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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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  1. Compatible Poisson structures on multiplicative quiver varieties

    math.SG 2023-10 unverdicted novelty 7.0

    Multiplicative quiver varieties carry a pencil of dimension ℓ(ℓ-1)/2 of compatible Poisson structures obtained by reduction from a pencil of Hamiltonian quasi-Poisson structures.