Noncommutative principal bundles through twist deformation

Aschieri, Paolo;Bieliavsky, Pierre;Pagani, Chiara;Schenkel, Alexander
(2017) Communications in Mathematical Physics — Vol. 352, n° 1, p. 287-344 (2016)

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Authors
  • Aschieri, Paoloorcid-logoUniversità del Piemonte Orientale
    Author
  • Bieliavsky, Pierreorcid-logoUCLouvain
    Author
  • Pagani, ChiaraGeorg-August-Universität Göttingen
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  • Schenkel, Alexanderorcid-logoUniversität Regensburg
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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.
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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 (Original work published 2016)