The gauge group of a noncommutative principal bundle and twist deformations

  • Paolo Aschieri

    Università del Piemonte Orientale, Alessandria, Italy
  • Giovanni Landi

    Università di Trieste, Italy
  • Chiara Pagani

    Università del Piemonte Orientale, Alessandria, Italy
The gauge group of a noncommutative principal bundle and twist deformations cover
Download PDF

A subscription is required to access this article.

Abstract

We study noncommutative principal bundles (Hopf–Galois extensions) in the context of coquasitriangular Hopf algebras and their monoidal category of comodule algebras. When the total space is quasi-commutative, and thus the base space subalgebra is central, we define the gauge group as the group of vertical automorphisms or equivalently as the group of equivariant algebra maps.We study Drinfeld twist (2-cocycle) deformations of Hopf–Galois extensions and show that the gauge group of the twisted extension is isomorphic to the gauge group of the initial extension. In particular, noncommutative principal bundles arising via twist deformation of commutative principal bundles have classical gauge group. We illustrate the theory with a few examples.

Cite this article

Paolo Aschieri, Giovanni Landi, Chiara Pagani, The gauge group of a noncommutative principal bundle and twist deformations. J. Noncommut. Geom. 14 (2020), no. 4, pp. 1501–1559

DOI 10.4171/JNCG/363