# Journal of Operator Theory

Volume 72, Issue 2, Fall 2014 pp. 557-576.

Groupoid
crossed products of continuous-trace $C^*$-algebras

**Authors**:
Erik van Erp (1) and Dana P. Williams (2)

**Author institution:** (1) Department of Mathematics, Dartmouth College, Hanover,
NH 03755, U.S.A.

(2) Department of Mathematics, Dartmouth College, Hanover, NH
03755, U.S.A.

**Summary: ** We show that if $(A,G,\alpha)$ is a groupoid
dynamical system with $A$
continuous trace, then the crossed product $A\rtimes_{\alpha}G$ is
Morita equivalent to the $C^*$-algebra $C^*(\uG,\uE)$ of a twist $\uE$
over a groupoid $\uG$ equivalent to $G$. This is a groupoid
analogue of the well known result for the crossed product of a group
acting on an elementary $C^*$-algebra.

**DOI: **http://dx.doi.org/10.7900/jot.2013sep04.2004

**Keywords: ** groupoid $C^*$-algebras, continuous-trace $C^*$-algebras,
crossed products

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