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