Skip to main content

Research Repository

Advanced Search

Noncommutative principal bundles through twist deformation

Aschieri, Paolo; Bieliavsky, Pierre; Pagani, Chiara; Schenkel, Alexander

Authors

Paolo Aschieri

Pierre Bieliavsky

Chiara Pagani



Abstract

We construct noncommutative principal bundles deforming principal bundles with a Drinfeld twist (2-cocycle). If the twist is associated with the structure group then we have a deformation of the fibers. If the twist is associated with the automorphism group of the principal bundle, then we obtain noncommutative deformations of the base space as well. Combining the two twist deformations we obtain noncommutative principal bundles with both noncommutative fibers and base space. More in general, the natural isomorphisms proving the equivalence of a closed monoidal category of modules and its twist related one are used to obtain new Hopf-Galois extensions as twists of Hopf-Galois extensions. A sheaf approach is also considered, and examples presented.

Citation

Aschieri, P., Bieliavsky, P., Pagani, C., & Schenkel, A. (2017). Noncommutative principal bundles through twist deformation. Communications in Mathematical Physics, 352(1), 287-344. https://doi.org/10.1007/s00220-016-2765-x

Journal Article Type Article
Acceptance Date Aug 29, 2016
Online Publication Date Nov 7, 2016
Publication Date May 31, 2017
Deposit Date Mar 2, 2017
Publicly Available Date Mar 29, 2024
Journal Communications in Mathematical Physics
Print ISSN 0010-3616
Electronic ISSN 1432-0916
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 352
Issue 1
Pages 287-344
DOI https://doi.org/10.1007/s00220-016-2765-x
Keywords noncommutative geometry, noncommutative principal bundles, Hopf-Galois extensions, cocycle twisting
Public URL https://nottingham-repository.worktribe.com/output/829391
Publisher URL http://link.springer.com/article/10.1007%2Fs00220-016-2765-x
Related Public URLs https://arxiv.org/abs/1604.03542
Additional Information The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-016-2765-x

Files





You might also like



Downloadable Citations