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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Bibliographic Details
Published in:Communications in mathematical physics 2017-05, Vol.352 (1), p.287-344
Main Authors: Aschieri, Paolo, Bieliavsky, Pierre, Pagani, Chiara, Schenkel, Alexander
Format: Article
Language:English
Subjects:
Bundles
Bundling
Classical and Quantum Gravitation
Complex Systems
Deformation
Mathematical and Computational Physics
Mathematical Physics
Modules
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-016-2765-x