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Responsabili:

Nel calendario si indicano i seminari di geometria algebrica e altre attività di interesse, organizzate dall'Università e dal Politecnico di Torino.

# Gauge group and Bisections on bialgebroid

## Data:

25/10/2022 - 10:30

Aula Lagrange

Xiao Han

## Categoria:

Seminari di Algebra e Geometria Algebrica

## Afferenza:

Queen Mary University of London

## Descrizione:

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.