Measured Quantum Groupoids Associated with Matched Pairs of Locally Compact Groupoids

TL;DR

This paper introduces a new class of measured quantum groupoids derived from matched pairs of locally compact groupoids with Haar systems, expanding the framework of quantum symmetries.

Contribution

It generalizes matched pairs from groups to locally compact groupoids and constructs new examples of measured quantum groupoids.

Findings

Established a framework for matched pairs of locally compact groupoids with Haar systems.

Provided explicit constructions of measured quantum groupoids from these matched pairs.

Extended the theory of quantum groupoids to a broader class of mathematical objects.

Abstract

Generalizing the notion of matched pair of groups, we define and study matched pairs of locally compact groupoids endowed with Haar systems, in order to give new examples of measured quantum groupoids.