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Noncommutative Principal Bundles Through Twist Deformation

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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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Authors and Affiliations

  1. Dipartimento di Scienze e Innovazione Tecnologica and INFN Torino, Università del Piemonte Orientale, Viale T. Michel 11, 15121, Alessandria, Italy

    Paolo Aschieri

  2. Institut de recherche en mathématique et physique, Université de Louvain, Chemin du Cyclotron 2 bte L7.01.02, 1348, Louvain-la-Neuve, Belgium

    Pierre Bieliavsky

  3. Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstraße 3-5, 37073, Göttingen, Germany

    Chiara Pagani

  4. Fakultät für Mathematik, Universität Regensburg, 93040, Regensburg, Germany

    Alexander Schenkel

Authors
  1. Paolo Aschieri
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  2. Pierre Bieliavsky
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  3. Chiara Pagani
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  4. Alexander Schenkel
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Corresponding author

Correspondence to Paolo Aschieri.

Additional information

Communicated by N. A. Nekrasov

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Aschieri, P., Bieliavsky, P., Pagani, C. et al. Noncommutative Principal Bundles Through Twist Deformation. Commun. Math. Phys. 352, 287–344 (2017). https://doi.org/10.1007/s00220-016-2765-x

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  • DOI: https://doi.org/10.1007/s00220-016-2765-x

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