
Journal of Lie Theory 32 (2022), No. 3, 737749 Copyright Heldermann Verlag 2022 A Cohomological Approach to the Existence Problem of Compact CliffordKlein Forms for Indecomposable PseudoRiemannian Symmetric Spaces Keiichi Maeta Graduate School of Mathematical Sciences, University of Tokyo, Japan velheimer@gmail.com We give examples of indecomposable but reducible pseudoRiemannian symmetric spaces of arbitrary signature which admit no compact CliffordKlein forms by a cohomological approach. We also show some series of even dimensional indecomposable but reducible pseudoRiemannian symmetric spaces of arbitrary signature admit compact CliffordKlein forms. We give another proof for the classification of indecomposable but reducible symmetric spaces with signature (2,2) which admit compact CliffordKlein forms which is proved in a forthcoming paper [Four dimensional compact Clifford–Klein forms of pseudoRiemannian symmetric spaces with signature (2, 2)] by a different approach. Keywords: Manifold locally modelled on a homogeneous space, CliffordKlein form, solvable symmetric spaces. MSC: 57S30, 17B56, 53C35, 53C50, 57T15. [ Fulltextpdf (206 KB)] for subscribers only. 