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arXiv · 1801.00832

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

Marius Ionescu·Alex Kumjian·Aidan Sims·Dana P. Williams
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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 \v{C}ech $2$-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.

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Marius Ionescu, Alex Kumjian, Aidan Sims, Dana P. Williams. 2018-01-02. The Dixmier-Douady Classes of Certain Groupoid $C^*$-Algebras with Continuous Trace. https://arxiv.org/abs/1801.00832

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