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Double Poisson algebras

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arxiv math/0410528 v4 pith:XE765E6U submitted 2004-10-25 math.QA math.RA

Michel Van den Bergh This is my paper · ORCID
classification math.QAmath.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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quasi-Poisson varieties from double quasi-Poisson algebras in types $B,C,D$

    math.RT 2026-05 unverdicted novelty 7.0 of 10

    Double quasi-Poisson brackets on associative algebras with involutive anti-automorphisms induce quasi-Poisson structures on twisted representation spaces over arbitrary semisimple bases, with applications to twisted q...

  2. Quartic BV structures in supercategories and modified necklace Lie bialgebras

    math.QA 2025-09 conditional novelty 7.0 of 10

    The augmented necklace Lie bialgebra, whose bracket and cobracket insert rather than remove involution pairs of arrows, is claimed to satisfy the IBL axioms and is witnessed by quartic Poisson/BV structures on represe...

  3. Compatible Poisson structures on multiplicative quiver varieties

    math.SG 2023-10 unverdicted novelty 7.0 of 10

    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.

  4. Double Transposed Poisson Algebras

    math.RT 2026-07 unverdicted novelty 6.0 of 10

    Double transposed Poisson algebras on unital associative algebras are governed by a single derivation to A tensor S(A over commutators), inducing GL_N-equivariant transposed Poisson structures on representation algebr...

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