Poisson manifolds with compatible pseudo-metric and pseudo-Riemannian Lie algebras
| dc.creator | Boucetta, Mohamed | |
| dc.date | 2002-06-10 | |
| dc.date.accessioned | 2026-07-07T04:49:01Z | |
| dc.date.available | 2026-07-07T04:49:01Z | |
| dc.description | The notion of Poisson manifold with compatible pseudo-metric was introduced by the author in [1]. In this paper, we introduce a new class of Lie algebras which we call a pseudo-Rieamannian Lie algebras. The two notions are strongly related: we prove that a linear Poisson structure on the dual of a Lie algebra has a compatible pseudo-metric if and only if the Lie algebra is a pseudo-Riemannian Lie algebra, and that the Lie algebra obtained by linearizing at a point a Poisson manifold with compatible pseudo-metric is a pseudo-Riemannian Lie algebra. Furthermore, we give some properties of the symplectic leaves of such manifolds, and we prove that every Poisson manifold with compatible metric (every Riemann-Lie algebra) is unimodular. As a final, we classify all pseudo-Riemannian Lie algebras of dimension 2 and 3. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0206102 | |
| dc.identifier | http://arxiv.org/abs/math/0206102 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64271 | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 53C30 | |
| dc.title | Poisson manifolds with compatible pseudo-metric and pseudo-Riemannian Lie algebras | |
| dc.type | text |