Non-connected Lie groups, twisted equivariant bundles and coverings

• Type: Article in International Scientific Journal
• Date: 2023

Authors

Barajas, G (Author) Other; Garcia-Prada, O (Author) Other; Gothen, PB (Author) FCUP; Riera, IMI (Author) Other

Journal

Title: Geometriae Dedicata

Vol. 217

ISSN: 0046-5755

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 0 Citations

Scopus

Other information

Authenticus ID: P-00X-RAA

DOI: 10.1007/s10711-022-00764-w

Abstract (EN): Let gamma be a finite group acting on a Lie group G. We consider a class of group extensions 1 -> G -> G -> gamma -> 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 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 G.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 41