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Semisimple symmetric spaces without compact manifolds locally modelled thereon. (English) Zbl 1320.53059

In an earlier work the author established a cohomological restriction to the existence of compact Clifford-Klein forms for reductive symmetric spaces. In this work, he applies a reformulation of this criterion in terms of Lie algebra cohomology to derive a classification of semi-simple, pseudo-Riemannian symmetric spaces which do not admit a compact Clifford-Klein form.

MSC:

53C35 Differential geometry of symmetric spaces
57S30 Discontinuous groups of transformations
17B56 Cohomology of Lie (super)algebras
22F30 Homogeneous spaces
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