Integrability and reduction of Poisson group actions

dc.creatorStefanini, Luca
dc.date2007-10-30
dc.date2007-11-01
dc.date.accessioned2026-07-07T08:39:38Z
dc.date.available2026-07-07T08:39:38Z
dc.descriptionIn 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.
dc.description20 pages, corrected misspellt preposition in the title
dc.identifierhttps://arxiv.org/abs/0710.5753
dc.identifierhttp://arxiv.org/abs/0710.5753
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141136
dc.subjectSymplectic Geometry
dc.subjectDifferential Geometry
dc.subject53D20 (Primary); 58H05, 18D05 (Secondary)
dc.titleIntegrability and reduction of Poisson group actions
dc.typetext

Files

Collections