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Non-commutative quasi-Hamiltonian spaces

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arxiv math/0703293 v1 pith:KT6N3DVB submitted 2007-03-10 math.QA

Michel Van den Bergh This is my paper · ORCID
classification math.QA
keywords non-commutativeanaloguesintroducedquasi-hamiltonianspacesalekseevalgebrasauthor
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abstract

In this paper we introduce non-commutative analogues for the quasi-Hamiltonian $G$-spaces introduced by Alekseev, Malkin and Meinrenken. We outline the connection with the non-commutative analogues of quasi-Poisson algebras which the author had introduced earlier.

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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. Double Poisson (vertex) algebra cohomology

    math.RT 2025-09 accept novelty 8.0 of 10

    The authors define a completed double Poisson cohomology valid for all double Poisson brackets, and introduce three cohomology theories for double Poisson vertex algebras, with representation functor compatibility.

  2. 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...

  3. Coupled double Poisson brackets

    math.QA 2026-05 unverdicted novelty 7.0 of 10

    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.

  4. 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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