Integrability of Poisson-Lie group actions

Abstract

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 $G/H$.

21 pages, further minor revisions; a contribution to the proceedings of the conference "Poisson 2008" (Poisson Geometry in Mathematics and Physics), to appear in Letters in Mathematical Physics

References in corpus (1)

• Integrability and reduction of Poisson group actions