Integrability of Poisson-Lie group actions

Details Integrability of Poisson-Lie group actions Integrability of Poisson-Lie group actions

2009-02-20

arxiv.org/abs/0902.3558v2

Mathematics

Differential Geometry

21 pages, further minor revisions; a contribution to the proceedings of the conference "Poisson 2008" (Poisson Geometry in Mat

Scientific paper

We establish a 1:1 correspondence between Poisson-Lie group actions on integrable Poisson manifolds and twisted multiplicative hamiltonian actions on source 1-connected symplectic groupoids. For an action of a Poisson-Lie group $G$ on a Poisson manifold $M$, we find an explicit description of the lifted hamiltonian action on the symplectic groupoid $\Sigma(M)$. We give applications of these results to the integration of Poisson quotients $M/G$, Lu-Weinstein quotients $\mu^{-1}(e)/G$ and Poisson homogeneous spaces $G/H$.

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