Integrability and reduction of Poisson group actions
| dc.creator | Stefanini, Luca | |
| dc.date | 2007-10-30 | |
| dc.date | 2007-11-01 | |
| dc.date.accessioned | 2026-07-07T08:39:38Z | |
| dc.date.available | 2026-07-07T08:39:38Z | |
| dc.description | 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. | |
| dc.description | 20 pages, corrected misspellt preposition in the title | |
| dc.identifier | https://arxiv.org/abs/0710.5753 | |
| dc.identifier | http://arxiv.org/abs/0710.5753 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141136 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 53D20 (Primary); 58H05, 18D05 (Secondary) | |
| dc.title | Integrability and reduction of Poisson group actions | |
| dc.type | text |