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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Main Authors: Aschieri, Paolo, Bieliavsky, Pierre, Pagani, Chiara, Schenkel, Alexander
Format: Article
Published: Springer 2016
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Online Access:https://eprints.nottingham.ac.uk/40999/
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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.
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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/