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February 2015 Semisimple symmetric spaces without compact manifolds locally modelled thereon
Yosuke Morita
Proc. Japan Acad. Ser. A Math. Sci. 91(2): 29-33 (February 2015). DOI: 10.3792/pjaa.91.29

Abstract

Let $G$ be a real reductive Lie group and $H$ a closed subgroup of $G$ which is reductive in $G$. In our earlier work it was shown that, if the homomorphism $i : H^{\bullet}(\mathfrak{g}_{\mathbf{C}}, \mathfrak{h}_{\mathbf{C}}; \mathbf{C}) \to H^{\bullet}(\mathfrak{g}_{\mathbf{C}},(\mathfrak{k}_{H})_{\mathbf{C}}; \mathbf{C})$ is not injective, there does not exist a compact manifold locally modelled on $G/H$. In this paper, we give a classification of the semisimple symmetric spaces $G/H$ for which $i$ is not injective. We also study the case when $G$ cannot be realised as a linear group.

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Yosuke Morita. "Semisimple symmetric spaces without compact manifolds locally modelled thereon." Proc. Japan Acad. Ser. A Math. Sci. 91 (2) 29 - 33, February 2015. https://doi.org/10.3792/pjaa.91.29

Information

Published: February 2015
First available in Project Euclid: 2 February 2015

zbMATH: 1320.53059
MathSciNet: MR3310968
Digital Object Identifier: 10.3792/pjaa.91.29

Subjects:
Primary: 53C15 , 57S30
Secondary: 17B56 , 22F30 , 53C30

Keywords: $(G,X)$-structure , Clifford–Klein form , invariant polynomial , local model , relative Lie algebra cohomology , Symmetric space

Rights: Copyright © 2015 The Japan Academy

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Vol.91 • No. 2 • February 2015
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