Semisimple symmetric spaces without compact manifolds locally modelled thereon

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Yosuke Morita¹ 

[1]Graduate School of Mathematical Science, The University of Tokyo

关键词: Local model;    ðG;    XÞ-structure;    Clifford–Klein form;    symmetric space;    relative Lie algebra cohomology;    invariant polynomial.;   

DOI  :  10.3792/pjaa.91.29

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

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.

【 授权许可】

Unknown