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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.09119 |
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| _version_ | 1866912160424132608 |
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| author | Bochenski, Maciej Tralle, Aleksy |
| author_facet | Bochenski, Maciej Tralle, Aleksy |
| contents | We find relations between real root decompositions of triples of Lie algebras corresponding to standard compact Clifford-Klein forms, under the assumption that these triples are not Lie algebra decompositions in the sense of Onishchik. This enables us to find new classes of homogeneous spaces of simple real Lie groups which do not admit standard compact Clifford-Klein forms. In particular, we show that proper R-regular subalgebras of simple real Lie algebras never generate homogeneous spaces which admit compact standard Cliffrod-Klein forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_09119 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Standard compact Clifford-Klein forms and Lie algebra decompositions Bochenski, Maciej Tralle, Aleksy Representation Theory 22E46 We find relations between real root decompositions of triples of Lie algebras corresponding to standard compact Clifford-Klein forms, under the assumption that these triples are not Lie algebra decompositions in the sense of Onishchik. This enables us to find new classes of homogeneous spaces of simple real Lie groups which do not admit standard compact Clifford-Klein forms. In particular, we show that proper R-regular subalgebras of simple real Lie algebras never generate homogeneous spaces which admit compact standard Cliffrod-Klein forms. |
| title | Standard compact Clifford-Klein forms and Lie algebra decompositions |
| topic | Representation Theory 22E46 |
| url | https://arxiv.org/abs/2212.09119 |