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arxiv: math/0006168 · v1 · submitted 2000-06-22 · 🧮 math.DG · math.QA

Quasi-Poisson Manifolds

classification 🧮 math.DG math.QA
keywords manifoldsinvariantquasi-poissonfieldassociatedbivectorbracketconcept
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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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