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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/195103
Non-connected Lie groups, twisted equivariant bundles and coverings
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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 $\hat{G}$.
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BARAJAS AYUSO, Guillermo, et al. Non-connected Lie groups, twisted equivariant bundles and coverings. Geometriae Dedicata. 2023. Vol. 217. ISSN 0046-5755. [consulted: 15 of October of 2026]. Available at: https://hdl.handle.net/2445/195103