Dirac geometry, quasi-Poisson actions and D/G-valued moment maps
Abstract
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.
Keywords
Cite
@article{arxiv.0710.0639,
title = {Dirac geometry, quasi-Poisson actions and D/G-valued moment maps},
author = {Henrique Bursztyn and Marius Crainic},
journal= {arXiv preprint arXiv:0710.0639},
year = {2008}
}
Comments
55 pages. v2: minor corrections, typos fixed; to appear in J. Differential Geometry