Noncommutative principal bundles through twist deformation

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.

58 pages. In print in CMP. Misprint corrected. An outline of the present work is in arXiv:1611.01493

References in corpus (3)

• Nonassociative geometry in quasi-Hopf representation categories I: Bimodules and their internal homomorphisms
• Quantisation of twistor theory by cocycle twist
• Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature

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