The Gauge Group of a Noncommutative Principal Bundle and Twist Deformations
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.
Keywords
Cite
@article{arxiv.1806.01841,
title = {The Gauge Group of a Noncommutative Principal Bundle and Twist Deformations},
author = {Paolo Aschieri and Giovanni Landi and Chiara Pagani},
journal= {arXiv preprint arXiv:1806.01841},
year = {2020}
}
Comments
v3: 42 pages. Scientific content unchanged. Presentation improved. Section 3 re-written. Several minor changes. To appear in J. Noncommut. Geom