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 Σ(M). We give applications of these results to the integration of Poisson quotients M/G, Lu-Weinstein quotients μ-1(e)/G and Poisson homogeneous spaces G/H.
- Poisson actions
- Twisted multiplicative
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics