Non-connected Lie groups, twisted equivariant bundles and coverings
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916283942961152 |
|---|---|
| author | Barajas, G. García-Prada, O. Gothen, P. B. Riera, I. Mundet i |
| author_facet | Barajas, G. García-Prada, O. Gothen, P. B. Riera, I. Mundet i |
| contents | Let $Γ$ be a finite group acting on a Lie group $G$. We consider a class of group extensions $1 \to G \to \hat{G} \to Γ\to 1$ defined by this action and a $2$-cocycle of $Γ$ with values in the centre of $G$. We establish and study a correspondence between $\hat{G}$-bundles on a manifold and twisted $Γ$-equivariant bundles with structure group $G$ on a suitable Galois $Γ$-covering of the manifold. We also describe this correspondence in terms of non-abelian cohomology. Our results apply, in particular, to the case of a compact or reductive complex Lie group $\hat{G}$, since such a group is always isomorphic to an extension as above, where $G$ is the connected component of the identity and $Γ$ is the group of connected components of $\hat{G}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_09022 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non-connected Lie groups, twisted equivariant bundles and coverings Barajas, G. García-Prada, O. Gothen, P. B. Riera, I. Mundet i Differential Geometry Algebraic Geometry Primary 14H60, Secondary 53C07, 58D29 Let $Γ$ be a finite group acting on a Lie group $G$. We consider a class of group extensions $1 \to G \to \hat{G} \to Γ\to 1$ defined by this action and a $2$-cocycle of $Γ$ with values in the centre of $G$. We establish and study a correspondence between $\hat{G}$-bundles on a manifold and twisted $Γ$-equivariant bundles with structure group $G$ on a suitable Galois $Γ$-covering of the manifold. We also describe this correspondence in terms of non-abelian cohomology. Our results apply, in particular, to the case of a compact or reductive complex Lie group $\hat{G}$, since such a group is always isomorphic to an extension as above, where $G$ is the connected component of the identity and $Γ$ is the group of connected components of $\hat{G}$. |
| title | Non-connected Lie groups, twisted equivariant bundles and coverings |
| topic | Differential Geometry Algebraic Geometry Primary 14H60, Secondary 53C07, 58D29 |
| url | https://arxiv.org/abs/2208.09022 |