On the structure of pseudo-Riemannian symmetric spaces

Abstract

Following our approach to metric Lie algebras developed in a previous paper we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semisimple. 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: That leads to a classification scheme of indecomposable nonsimple 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 and Parker and to Neukirchner).