On Poisson actions of compact Lie groups on symplectic manifolds
| dc.creator | Alekseev, Anton Yu. | |
| dc.date | 1996-02-01 | |
| dc.date.accessioned | 2026-07-07T09:12:42Z | |
| dc.date.available | 2026-07-07T09:12:42Z | |
| dc.description | Let $G_¶$ be a compact simple Poisson-Lie group equipped with a Poisson structure $¶$ and $(M, ø)$ be a symplectic manifold. Assume that $M$ carries a Poisson action of $G_¶$ and there is an equivariant moment map in the sense of Lu and Weinstein which acts to the dual Poisson-Lie group $G^*_¶$, $\m: M\rightarrow G^*_¶$. We prove that $M$ always possesses another symplectic form $\to$ so that the $G$-action preserves $\tildeø$ and there is a new moment map $μ= e^{-1} \circ \m: M\rightarrow \g^*$. Here $e$ is a universal (independent of $M$) invertible equivariant map $e: \g^*\rightarrow G^*_¶$. We suggest new short proves of the convexity theorem for the Poisson-Lie moment map, Poisson reduction theorem and the Ginzburg-Weinstein theorem on the isomorphism of $\g^*$ and $G^*_¶$ as Poisson spaces. | |
| dc.description | LaTeX file, 16 pages | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9602001 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9602001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152108 | |
| dc.subject | Differential Geometry | |
| dc.subject | Quantum Algebra | |
| dc.title | On Poisson actions of compact Lie groups on symplectic manifolds | |
| dc.type | text |