Morita equivalence of measured quantum groupoids: Application to deformation of measured quantum groupoids by 2-cocycles

TL;DR

This paper extends Morita equivalence concepts from quantum groups to measured quantum groupoids and explores their deformation via 2-cocycles, broadening the understanding of quantum symmetries.

Contribution

It generalizes Morita equivalence and deformation techniques from quantum groups to measured quantum groupoids, providing new tools for their analysis.

Findings

Established Morita equivalence for measured quantum groupoids.

Developed a deformation framework using 2-cocycles.

Extended linking constructions to the quantum groupoid setting.

Abstract

In a recent article of Kenny De Commer, was investigated a Morita equivalence between locally compact quantum groups, in which a measured quantum groupoid, of basis $\mathbb{C}^2$, was constructed as a linking object. Here, we generalize all these constructions and concepts to the level of measured quantum groupoids. As for locally compact quantum groups, we apply this construction to the deformation of a measured quantum groupoid by a 2-cocycle.