Journal of Lie Theory 32 (2022), No. 3, 737--749
Copyright Heldermann Verlag 2022
A Cohomological Approach to the Existence Problem of Compact Clifford-Klein Forms for Indecomposable Pseudo-Riemannian Symmetric Spaces
Keiichi Maeta
Graduate School of Mathematical Sciences, University of Tokyo, Japan
velheimer@gmail.com
We give examples of indecomposable but reducible pseudo-Riemannian symmetric spaces of arbitrary signature which admit no compact Clifford-Klein forms by a cohomological approach. We also show some series of even dimensional indecomposable but reducible pseudo-Riemannian symmetric spaces of arbitrary signature admit compact Clifford-Klein forms. We give another proof for the classification of indecomposable but reducible symmetric spaces with signature (2,2) which admit compact Clifford-Klein forms which is proved in a forthcoming paper [Four dimensional compact Clifford–Klein forms of pseudo-Riemannian symmetric spaces with signature (2, 2)] by a different approach.
Keywords: Manifold locally modelled on a homogeneous space, Clifford-Klein form, solvable symmetric spaces.
MSC: 57S30, 17B56, 53C35, 53C50, 57T15.
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