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http://hdl.handle.net/2445/195103
Title: | Non-connected Lie groups, twisted equivariant bundles and coverings |
Author: | Barajas Ayuso, Guillermo García-Prada, Oscar Gothen, Peter Mundet i Riera, Ignasi |
Keywords: | Grups de Lie Corbes algebraiques Geometria diferencial Anàlisi global (Matemàtica) Lie groups Algebraic curves Differential geometry Global analysis (Mathematics) |
Issue Date: | 18-Jan-2023 |
Publisher: | Springer Verlag |
Abstract: | Let $\Gamma$ be a finite group acting on a Lie group $G$. We consider a class of group extensions $1 \rightarrow G \rightarrow \hat{G} \rightarrow \Gamma \rightarrow 1$ defined by this action and a 2-cocycle of $\Gamma$ with values in the centre of $G$. We establish and study a correspondence between $\hat{G}$-bundles on a manifold and twisted $\Gamma$-equivariant bundles with structure group $G$ on a suitable Galois $\Gamma$-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 $G$, since such a group is always isomorphic to an extension as above, where $G$ is the connected component of the identity and $\Gamma$ is the group of connected components of $\hat{G}$. |
Note: | Reproducció del document publicat a: https://doi.org/10.1007/s10711-022-00764-w |
It is part of: | Geometriae Dedicata, 2023, vol. 217 |
URI: | http://hdl.handle.net/2445/195103 |
Related resource: | https://doi.org/10.1007/s10711-022-00764-w |
ISSN: | 0046-5755 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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