Cohomologies of difference Lie groups and van Est theorem
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916171205312512 |
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| author | Jiang, Jun Li, Yunnan Sheng, Yunhe |
| author_facet | Jiang, Jun Li, Yunnan Sheng, Yunhe |
| contents | A difference Lie group is a Lie group equipped with a difference operator, equivalently a crossed homomorphism with respect to the adjoint action. In this paper, first we introduce the notion of a representation of a difference Lie group, and establish the relation between representations of difference Lie groups and representations of difference Lie algebras via differentiation and integration. Then we introduce a cohomology theory for difference Lie groups and justify it via the van Est theorem. Finally, we classify abelian extensions of difference Lie groups using the second cohomology group as applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_11716 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Cohomologies of difference Lie groups and van Est theorem Jiang, Jun Li, Yunnan Sheng, Yunhe Rings and Algebras K-Theory and Homology Representation Theory 13N99, 17B40, 17B56, 20J06 A difference Lie group is a Lie group equipped with a difference operator, equivalently a crossed homomorphism with respect to the adjoint action. In this paper, first we introduce the notion of a representation of a difference Lie group, and establish the relation between representations of difference Lie groups and representations of difference Lie algebras via differentiation and integration. Then we introduce a cohomology theory for difference Lie groups and justify it via the van Est theorem. Finally, we classify abelian extensions of difference Lie groups using the second cohomology group as applications. |
| title | Cohomologies of difference Lie groups and van Est theorem |
| topic | Rings and Algebras K-Theory and Homology Representation Theory 13N99, 17B40, 17B56, 20J06 |
| url | https://arxiv.org/abs/2210.11716 |