IUMJ

Title: GCR and CCR groupoid $C*$-algebras

Authors: Lisa Orloff Clark

Issue: Volume 56 (2007), Issue 5, 2087-2110

Abstract:

Suppose $G$ is a second countable, locally compact, Hausdorff groupoid with a fixed left Haar system. Let $G^0/G$ denote the orbit space of $G$ and $C^{*}(G)$ denote the groupoid $C^{*}$-algebra. Suppose that the isotropy groups of $G$ are amenable. We show that $C^{*}(G)$ is CCR if and only if $G^0/G$ is a $T_1$ topological space and all of the isotropy groups are CCR. We also show that $C^{*}(G)$ is GCR if and only if $G^0/G$ is a $T_0$ topological space and all of the isotropy groups are GCR.