# Journal of Operator Theory

Volume 81, Issue 2, Spring 2019 pp. 407-431.

The Dixmier-Douady classes of certain
groupoid $C^{*}$-algebras with continuous trace

**Authors**:
Marius Ionescu (1), Alex Kumjian (2), Aidan Sims (3),
Dana P. Williams (4)

**Author institution:**(1) Department of Mathematics, United States
Naval Academy, Annapolis, MD 21402 U.S.A.

(2) Department of Mathematics, University of
Nevada, Reno NV 89557 U.S.A.

(3) School of Mathematics and Applied Statistics,
University of Wollongong, NSW 2522, Australia

(4) Department of
Mathematics, Dartmouth College, Hanover, NH 03755-3551 U.S.A.

**Summary: **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.

**DOI: **http://dx.doi.org/10.7900/jot.2018mar07.2209

**Keywords: **Dixmier--Douady class, groupoid $C^*$-algebras, continuous-trace
$C^*$-algebras

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