# Journal of Operator Theory

Volume 89, Issue 1, Winter 2023  pp. 249-283.

Abelian twisted groupoid extensions

Authors:  Jean Renault
Author institution:Institut Denis Poisson (UMR 7013), CNRS et Universite d'Orleans, 45067 Orleans Cedex 2, France

Summary: This article gives a decomposition of the $C^*$-algebra of a twisted locally compact groupoid with Haar system in presence of a normal subgroupoid over which the twist is abelian. One obtains then an equivariant Gelfand isomorphism onto another twisted groupoid $C^*$-algebra. This is applied to $C^*$-algebraic deformation quantization and to multiplier representations of locally compact abelian groups.

DOI: http://dx.doi.org/10.7900/jot.2021may24.2366
Keywords: groupoid extension, twist, Mackey machine, multiplier representation