The Dixmier-Douady classes of certain groupoid C∗-algebras with continuous trace

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 Cech 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 etale equivalence relations.