A Cohomological Approach to the Existence Problem of Compact Clifford-Klein Forms for Indecomposable Pseudo-Riemannian Symmetric Spaces

K. Maeta

doi:10.5802/jolt.1249

K. Maeta

Journal of Lie Theory, Volume 32 (2022) no. 3, pp. 737-749

Abstract

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 CliffordKlein forms of pseudo-Riemannian symmetric spaces with signature (2, 2)] by a different approach.

Zbl

DOI: 10.5802/jolt.1249

Classification: 57S30, 17B56, 53C35, 53C50, 57T15
Keywords: Manifold locally modelled on a homogeneous space, Clifford-Klein form, solvable symmetric spaces

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     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},
     doi = {10.5802/jolt.1249},
     zbl = {1497.57046},
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}

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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, Volume 32 (2022) no. 3, pp. 737-749. doi: 10.5802/jolt.1249

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