Integrability of Poisson-Lie group actions

2009/02/20 by Fernandes, Rui Loja, Ponte, David Iglesias
#53D17 #53D20 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.0902.3558

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 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.

Related

• Integrability and reduction of Poisson group actions
• Intégration symplectique des variétés de Poisson régulières
• Induction of Hamiltonian Poisson actions
• On Poisson actions of compact Lie groups on symplectic manifolds
• Lie-Poisson integrators