The C*-algebra of a twisted groupoid extension

TL;DR

This paper extends the theory of C*-algebras to twisted groupoid extensions, providing a decomposition in the presence of a normal subgroupoid and exploring applications to deformation quantization and multiplier representations.

Contribution

It generalizes previous results to twisted groupoids, offering a new decomposition approach for their C*-algebras with applications to quantization and representation theory.

Findings

Decomposition of C*-algebra for twisted groupoid extensions

Application to deformation quantization

Analysis of multiplier representations of abelian groups

Abstract

This article extends the main results of the publication arXiv:2001.01312 to the case of a twisted groupoid. More precisely, it gives a decomposition of the C*-algebra of a twisted locally compact groupoid with Haar system in presence of a normal subgroupoid. When the normal subgroupoid and the twist over it are abelian, one obtains another twisted groupoid C*-algebra. This is applied to C*-algebraic deformation quantization and to multiplier representations of locally compact abelian groups.