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.

中文翻译：

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非交换主束的规范群和扭曲变形

我们在拟三角Hopf代数及其协模代数的单项类别的背景下研究非交换主束（Hopf–Galois扩展）。当总空间是准可交换的，因此基础空间子代数处于中心时，我们将规范组定义为垂直自同构组或等价代数映射组。我们研究了Drinfeld扭曲（2-cocycle）变形Hopf–Galois扩展并显示扭曲扩展的规范组与初始扩展的规范组同构。特别地，通过可交换主束的扭曲变形产生的非可交换主束具有经典规格组。我们用几个例子来说明这个理论。