Integrability of Poisson-Lie group actions

Rui Loja Fernandes, David Iglesias Ponte

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)137-159
Number of pages23
JournalLetters in Mathematical Physics
Volume90
Issue number1
DOIs
StatePublished - Nov 2009
Externally publishedYes

Keywords

  • Integrability
  • Poisson actions
  • Twisted multiplicative

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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