Integrability and reduction of Poisson group actions

Abstract

In this paper we study Poisson actions of complete Poisson groups, without any connectivity assumption or requiring the existence of a momentum map. For any complete Poisson group $G$ with dual $G^{\star }$ we obtain a suitably connected integrating symplectic double groupoid $\calS$. As a consequence, the cotangent lift of a Poisson action on an integrable Poisson manifold $P$ can be integrated to a Poisson action of the symplectic groupoid $\poidd{\calS}{G^\star}$ on the symplectic groupoid for $P$. Finally, we show that the quotient Poisson manifold $P/G$ is also integrable, giving an explicit construction of a symplectic groupoid for it, by a reduction procedure on an associated morphism of double Lie groupoids.

20 pages, corrected misspellt preposition in the title

Cited by in corpus (2)

• On Morphic Actions and Integrability of LA-Groupoids
• Integrability of Poisson-Lie group actions