Noncommutative principal bundles through twist deformation

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

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 2, 2017
• 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
• Contract Date: Mar 2, 2017