Dirac geometry, quasi-Poisson actions and D/G-valued moment maps

Details Dirac geometry, quasi-Poisson actions and D/G-valued moment maps Dirac geometry, quasi-Poisson actions and D/G-valued moment maps

2007-10-02

arxiv.org/abs/0710.0639v2

Mathematics

Differential Geometry

55 pages. v2: minor corrections, typos fixed; to appear in J. Differential Geometry

Scientific paper

We study Dirac structures associated with Manin pairs (\d,\g) and give a Dirac geometric approach to Hamiltonian spaces with D/G-valued moment maps, originally introduced by Alekseev and Kosmann-Schwarzbach in terms of quasi-Poisson structures. We explain how these two distinct frameworks are related to each other, proving that they lead to isomorphic categories of Hamiltonian spaces. We stress the connection between the viewpoint of Dirac geometry and equivariant differential forms. The paper discusses various examples, including q-Hamiltonian spaces and Poisson-Lie group actions, explaining how presymplectic groupoids are related to the notion of "double" in each context.

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