Quasi-Hamiltonian groupoids and multiplicative Manin pairs
arXiv:0911.2179 · doi:10.1093/imrn/rnq170
Abstract
We reformulate notions from the theory of quasi-Poisson g-manifolds in terms of graded Poisson geometry and graded Poisson-Lie groups and prove that quasi-Poisson g-manifolds integrate to quasi-Hamiltonian g-groupoids. We then interpret this result within the theory of Dirac morphisms and multiplicative Manin pairs, to connect our work with more traditional approaches, and also to put it into a wider context suggesting possible generalizations.
39 pages
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Cited by in corpus (17)
- VB-groupoids and representation theory of Lie groupoids
- Lie theory of multiplicative tensors
- LA-Courant algebroids and their applications
- N-manifolds of degree 2 and metric double vector bundles
- Multiplicative Dirac structures
- Dirac Geometry of the Holonomy Fibration
- Multiple vector bundles: cores, splittings and decompositions
- Modular Classes of Lie Groupoid Representations up to Homotopy
- On the T-leaves of some Poisson structures related to products of flag varieties
- Mixed product Poisson structures associated to Poisson Lie groups and Lie bialgebras
- The Classification of Dirac Homogeneous Spaces
- On the reduced space of multiplicative multivectors
- The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular -Matrix
- Affine structures on Lie groupoids
- Reduction of symplectic groupoids and quotients of quasi-Poisson manifolds
- Quasi Poisson structures, weakly quasi Hamiltonian structures, and Poisson geometry of various moduli spaces
- Pseudo-Dirac Structures