On the Structure of Complex Homogeneous Supermanifolds
| dc.creator | Vishnyakova, E. G. | |
| dc.date | 2008-11-16 | |
| dc.date.accessioned | 2026-07-07T10:18:45Z | |
| dc.date.available | 2026-07-07T10:18:45Z | |
| dc.description | For a Lie group $G$ and a closed Lie subgroup $H\subset G$, it is well known that the coset space $G/H$ can be equipped with the structure of a manifold homogeneous under $G$ and that any $G$-homogeneous manifold is isomorphic to one of this kind. An interesting problem is to find an analogue of this result in the case of supermanifolds. In the classical setting, $G$ is a real or a complex Lie group and $G/H$ is a real and, respectively, a complex manifold. Now, if $G$ is a real Lie supergroup and $H\subset G$ is a closed Lie subsupergroup, there is a natural way to consider $G/H$ as a supermanfold. Furthermore, any $G$-homogeneous real supermanifold can be obtained in this way, see \cite{Kostant}. The goal of this paper is to give a proof of this result in the complex case. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/0811.2581 | |
| dc.identifier | http://arxiv.org/abs/0811.2581 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174296 | |
| dc.subject | Differential Geometry | |
| dc.subject | 32C11 | |
| dc.title | On the Structure of Complex Homogeneous Supermanifolds | |
| dc.type | text |