Generalised Twisted Groupoids and their C*-algebras

Abstract

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

This revised version removes the condition that a $\hat{I}“$-twist need be locally trivial, and the results are updated accordingly. 21 pages