Group orbits and regular partitions of Poisson manifolds
| dc.creator | Lu, Jiang-Hua | |
| dc.creator | Yakimov, Milen | |
| dc.date | 2006-09-26 | |
| dc.date | 2007-02-15 | |
| dc.date.accessioned | 2026-07-07T07:46:51Z | |
| dc.date.available | 2026-07-07T07:46:51Z | |
| dc.description | We study a large class of Poisson manifolds, derived from Manin triples, for which we construct explicit partitions into regular Poisson submanifolds by intersecting certain group orbits. Examples include all varieties ${\mathcal L}$ of Lagrangian subalgebras of reductive quadratic Lie algebras $\d$ with Poisson structures defined by Lagrangian splittings of $\d$. In the special case of $\g \oplus \g$, where $\g$ is a complex semi-simple Lie algebra, we explicitly compute the ranks of the Poisson structures on ${\mathcal L}$ defined by arbitrary Lagrangian splittings of ${\mathfrak g} \oplus {\mathfrak g}$. Such Lagrangian splittings have been classified by P. Delorme, and they contain the Belavin--Drinfeld splittings as special cases. | |
| dc.description | 23 pages, AMS Latex, minor changes in v.2 | |
| dc.identifier | https://arxiv.org/abs/math/0609732 | |
| dc.identifier | http://arxiv.org/abs/math/0609732 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123964 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Representation Theory | |
| dc.title | Group orbits and regular partitions of Poisson manifolds | |
| dc.type | text |