2020/01/05 by Ionescu, Marius, Kumjian, Alex, Renault, Jean N. +2
#FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2001.01312
Given a normal subgroup bundle \mathcal A of the isotropy bundle of a groupoid Σ, we obtain a twisted action of the quotient groupoid Σ/\mathcal A on the bundle of group C^*-algebras determined by \mathcal A whose twisted crossed product recovers the groupoid C^*-algebra C^*(Σ). Restricting to the case where \mathcal A is abelian, we describe C^*(Σ) as the C^*-algebra associated to a \mathbf T-groupoid over the tranformation groupoid obtained from the canonical action of Σ/\mathcal A on the Pontryagin dual space of \mathcal A. We give some illustrative examples of this result.