Gauge group and Bisections on bialgebroid [1]

Abstract:

We study the Ehresmann–Schauenburg bialgebroid of a noncommutative principal bundle as a quantization of the gauge groupoid of a classical principal bundle.
We show that the gauge group of the noncommutative bundle is isomorphic to the group of bisections of the bialgebroid, and we give a crossed module
structure for the bisections and the automorphisms of the bialgebroid. Example illustrating this construction include: a monopole bundle over a quantum spheres. Moreover, we are
going to construct a 2-cocycle \tilde{\sigma} on an ES-bialgebroid from a cleft Hopf Galois extension. We show that in the case of associative type, L(B#_{σ}H, H) = L(B#H)^{\tilde{\sigma}}.

This talk is based on a joint work with Giovanni Landi.