Geodesic
A Cohomological Approach to the Existence Problem of Compact Clifford-Klein Forms for Indecomposable Pseudo-Riemannian Symmetric Spaces
Journal of Lie theory, Tome 32 (2022) no. 3, pp. 737-749
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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.
Classification : 57S30, 17B56, 53C35, 53C50, 57T15
Mots-clés : Manifold locally modelled on a homogeneous space, Clifford-Klein form, solvable symmetric spaces 
@article{JLT_2022_32_3_JLT_2022_32_3_a5,
     author = {K. Maeta},
     title = {A {Cohomological} {Approach} to the {Existence} {Problem} of {Compact} {Clifford-Klein} {Forms} for {Indecomposable} {Pseudo-Riemannian} {Symmetric} {Spaces}},
     journal = {Journal of Lie theory},
     pages = {737--749},
     year = {2022},
     volume = {32},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2022_32_3_JLT_2022_32_3_a5/}
}
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K. Maeta. A Cohomological Approach to the Existence Problem of Compact Clifford-Klein Forms for Indecomposable Pseudo-Riemannian Symmetric Spaces. Journal of Lie theory, Tome 32 (2022) no. 3, pp. 737-749. http://geodesic.mathdoc.fr/item/JLT_2022_32_3_JLT_2022_32_3_a5/