TY - RPRT
T1 - On the gauge group of Galois objects
Y1 - 2020
A1 - Xiao Han
A1 - Giovanni Landi
AB - We 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.
UR - https://arxiv.org/abs/2002.06097
ER -