The Dixmier-Douady Classes of Certain Groupoid C^*-Algebras with Continuous Trace

2018/01/02 by Ionescu, Marius, Kumjian, Alex, Sims, Aidan +1
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1801.00832

Abstract

Given a locally compact abelian group G, we give an explicit formula for the Dixmier--Douady invariant of the C^*-algebra of the groupoid extension associated to a Čech 2-cocycle in the sheaf of germs of continuous G-valued functions. We then exploit the blow-up construction for groupoids to extend this to some more general central extensions of étale equivalence relations.

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