On the structure of pseudo-Riemannian symmetric spaces
| dc.creator | Kath, Ines | |
| dc.creator | Olbrich, Martin | |
| dc.date | 2004-08-18 | |
| dc.date.accessioned | 2026-07-07T05:11:22Z | |
| dc.date.available | 2026-07-07T05:11:22Z | |
| dc.description | Following our approach to metric Lie algebras developed in math.DG/0312243 we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated with orthogonal modules of Lie algebras with involution. Then we construct a functorial assignment which sends a pseudo-Riemannian symmetric space M to a triple consisting of (i) a Lie algebra with involution (of dimension much smaller than the dimension of the transvection group of M), (ii) a semi-simple orthogonal module of the Lie algebra with involution, and (iii) a quadratic cohomology class of this module. That leads to a classification scheme of indecomposable non-simple pseudo-Riemannian symmetric spaces. In addition, we obtain a full classification of symmetric spaces of index 2 (thereby completing and correcting in part earlier classification results due to Cahen/Parker and Neukirchner math.DG/0301326). | |
| dc.description | 37 pages | |
| dc.identifier | https://arxiv.org/abs/math/0408249 | |
| dc.identifier | http://arxiv.org/abs/math/0408249 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72218 | |
| dc.subject | Differential Geometry | |
| dc.subject | Representation Theory | |
| dc.subject | 53C35; 53C50; 17B56 | |
| dc.title | On the structure of pseudo-Riemannian symmetric spaces | |
| dc.type | text |