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Quasi-Poisson Manifolds

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arxiv math/0006168 v1 pith:G5M7KLAI submitted 2000-06-22 math.DG math.QA

Anton Alekseev , Yvette Kosmann-Schwarzbach , Eckhard Meinrenken This is my paper · ORCID
classification math.DGmath.QA
keywords manifoldsinvariantquasi-poissonfieldassociatedbivectorbracketconcept
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abstract

A quasi-Poisson manifold is a G-manifold equipped with an invariant bivector field whose Schouten bracket is the trivector field generated by the invariant element in $\wedge^3 \g$ associated to an invariant inner product. We introduce the concept of the fusion for such manifolds, and we relate quasi-Poisson manifolds to the previously introduced quasi-Hamiltonian manifolds with group-valued moment maps.

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Cited by 3 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. Integrable systems from Poisson reductions of generalized Hamiltonian torus actions

    math-ph 2025-07 unverdicted novelty 7.0 of 10

    Develops sufficient conditions for Poisson reduction of generalized Hamiltonian torus actions to preserve integrability and applies them to open problems on Lie group doubles and flat-connection moduli spaces.

  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.

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