Proceedings of the Japan Academy, Series A, Mathematical Sciences

Classification of irreducible symmetric spaces which admit standard compact Clifford–Klein forms

Koichi Tojo

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Abstract

We give a classification of irreducible symmetric spaces which admit standard compact Clifford–Klein forms. The method uses representation theory over the real number field and the criterion for properness and cocompactness of the action on homogeneous spaces due to T. Kobayashi.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 95, Number 2 (2019), 11-15.

Dates
First available in Project Euclid: 1 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.pja/1548990026

Digital Object Identifier
doi:10.3792/pjaa.95.11

Mathematical Reviews number (MathSciNet)
MR3905124

Subjects
Primary: 22F30: Homogeneous spaces {For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40} 57S30: Discontinuous groups of transformations
Secondary: 22E46: Semisimple Lie groups and their representations 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15] 53C35: Symmetric spaces [See also 32M15, 57T15]

Keywords
Clifford–Klein form tangential homogeneous space symmetric space properness criterion discontinuous group real representation

Citation

Tojo, Koichi. Classification of irreducible symmetric spaces which admit standard compact Clifford–Klein forms. Proc. Japan Acad. Ser. A Math. Sci. 95 (2019), no. 2, 11--15. doi:10.3792/pjaa.95.11. https://projecteuclid.org/euclid.pja/1548990026


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