Generalised Twisted Groupoids and their C*-algebras

TL;DR

This paper generalizes the concept of twisted groupoid C*-algebras by replacing the circle group with a more general abelian group, showing that these generalized algebras are isomorphic to the classical twisted groupoid C*-algebras.

Contribution

It introduces a broader class of twists for groupoid C*-algebras using abelian groups and proves their isomorphism to standard twisted groupoid C*-algebras.

Findings

Generalized twists are isomorphic to classical twists.

Extension to abelian groups broadens the framework.

Provides a unified approach to twisted groupoid C*-algebras.

Abstract

We consider a locally compact Hausdorff groupoid $G$, and twist by a more general locally compact Hausdorff abelian group $\Gamma$ rather than the complex unit circle $\mathbb{T}$. We investigate the construction of $C^*$-algebras in analogue to the usual twisted groupoid $C^*$-algebras, and we show that, in fact, any $\Gamma$-twisted groupoid $C^*$-algebra is isomorphic to a usual twisted groupoid $C^*$-algebra.