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Double Poisson algebras

· 2004 · math.QA · arXiv math/0410528

3 Pith papers cite this work. Polarity classification is still indexing.

3 Pith papers citing it
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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.

fields

math.RT 2 math.SG 1

years

2026 2 2023 1

verdicts

UNVERDICTED 3

representative citing papers

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

math.RT · 2026-05-22 · unverdicted · novelty 7.0

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 quiver varieties and Hopf algebras with Fox pairings.

Double Transposed Poisson Algebras

math.RT · 2026-07-01 · unverdicted · novelty 6.0

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 algebras and their invariants via trace maps.

citing papers explorer

Showing 3 of 3 citing papers.

  • Quasi-Poisson varieties from double quasi-Poisson algebras in types $B,C,D$ math.RT · 2026-05-22 · unverdicted · none · ref 31 · internal anchor

    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 quiver varieties and Hopf algebras with Fox pairings.

  • Compatible Poisson structures on multiplicative quiver varieties math.SG · 2023-10-28 · unverdicted · none · ref 40 · internal anchor

    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.

  • Double Transposed Poisson Algebras math.RT · 2026-07-01 · unverdicted · none · ref 12 · internal anchor

    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 algebras and their invariants via trace maps.