00996nas a2200121   4500008004100000245004100041210003400082260001200116520067500128100001400803700002000817856003700837       2020                        eng d00aOn the gauge group of Galois objects0 agauge group of Galois objects  c03/20203 aWe study the Ehresmann--Schauenburg bialgebroid of a noncommutative principal bundle as a quantization of the classical gauge groupoid of a principal bundle. When the base algebra is in the centre of the total space algebra, the gauge group of the noncommutative principal bundle is isomorphic to the group of bisections of the bialgebroid. In particular we consider Galois objects (non-trivial noncommutative bundles over a point in a sense) for which the bialgebroid is a Hopf algebra. For these we give a crossed module structure for the bisections and the automorphisms of the bialgebroid. Examples include Galois objects of group Hopf algebras and of Taft algebras.1 aHan, Xiao1 aLandi, Giovanni  uhttps://arxiv.org/abs/2002.06097