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Quasi-Poisson structures on representation spaces of surfaces

· 2012 · math.GT · arXiv 1205.4898

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

3 Pith papers citing it
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abstract

Given an oriented surface S with base point * on the boundary, we introduce for all N>0, a canonical quasi-Poisson bracket on the space of N-dimensional linear representations of \pi_1(S,*). Our bracket extends the well-known Poisson bracket on GL_N-invariant functions on this space. Our main tool is a natural structure of a quasi-Poisson double algebra (in the sense of M. Van den Bergh) on the group algebra of \pi_1(S,*).

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math.QA 1 math.RT 1 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.

Coupled double Poisson brackets

math.QA · 2026-05-17 · unverdicted · novelty 7.0

Introduces coupled double Poisson brackets, proves bijection to wheeled Poisson brackets, and gives correspondences to Poisson-left-pre-Lie algebras and Yang-Baxter solutions on free polynomial algebras.

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 23 · 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.

  • Coupled double Poisson brackets math.QA · 2026-05-17 · unverdicted · none · ref 80 · internal anchor

    Introduces coupled double Poisson brackets, proves bijection to wheeled Poisson brackets, and gives correspondences to Poisson-left-pre-Lie algebras and Yang-Baxter solutions on free polynomial algebras.

  • Compatible Poisson structures on multiplicative quiver varieties math.SG · 2023-10-28 · unverdicted · none · ref 32 · 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.