Noncommutative principal bundles through twist deformation
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 no...
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| Format: | Article |
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Springer
2016
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| Online Access: | https://eprints.nottingham.ac.uk/40999/ |
| _version_ | 1848796174636548096 |
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| author | Aschieri, Paolo Bieliavsky, Pierre Pagani, Chiara Schenkel, Alexander |
| author_facet | Aschieri, Paolo Bieliavsky, Pierre Pagani, Chiara Schenkel, Alexander |
| author_sort | Aschieri, Paolo |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:43:47Z |
| format | Article |
| id | nottingham-40999 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:47Z |
| publishDate | 2016 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-409992020-05-04T18:21:49Z https://eprints.nottingham.ac.uk/40999/ Noncommutative principal bundles through twist deformation Aschieri, Paolo Bieliavsky, Pierre Pagani, Chiara Schenkel, Alexander 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. Springer 2016-11-09 Article PeerReviewed Aschieri, Paolo, Bieliavsky, Pierre, Pagani, Chiara and Schenkel, Alexander (2016) Noncommutative principal bundles through twist deformation. Communications in Mathematical Physics . pp. 1-58. ISSN 1432-0916 noncommutative geometry noncommutative principal bundles Hopf-Galois extensions cocycle twisting http://link.springer.com/article/10.1007%2Fs00220-016-2765-x doi:10.1007/s00220-016-2765-x doi:10.1007/s00220-016-2765-x |
| spellingShingle | noncommutative geometry noncommutative principal bundles Hopf-Galois extensions cocycle twisting Aschieri, Paolo Bieliavsky, Pierre Pagani, Chiara Schenkel, Alexander Noncommutative principal bundles through twist deformation |
| title | Noncommutative principal bundles through twist deformation |
| title_full | Noncommutative principal bundles through twist deformation |
| title_fullStr | Noncommutative principal bundles through twist deformation |
| title_full_unstemmed | Noncommutative principal bundles through twist deformation |
| title_short | Noncommutative principal bundles through twist deformation |
| title_sort | noncommutative principal bundles through twist deformation |
| topic | noncommutative geometry noncommutative principal bundles Hopf-Galois extensions cocycle twisting |
| url | https://eprints.nottingham.ac.uk/40999/ https://eprints.nottingham.ac.uk/40999/ https://eprints.nottingham.ac.uk/40999/ |