Groupoid \(C^*\)-algebras with Hausdorff spectrum

Authors

  • G. Goehle Western Carolina University

Keywords:

groupoids, C*-algebras

Abstract

Suppose $G$ is a second countable, locally compact Hausdorff groupoid with abelian stabilizer subgroups and a Haar system. We provide necessary and sufficient conditions for the groupoid $C^*$-algebra to have Hausdorff spectrum. In particular we show that the spectrum of $C^*(G)$ is Hausdorff if and only if the stabilizers vary continuously with respect to the Fell topology, the orbit space $G\unit/G$ is Hausdorff, and, given convergent sequences $\chi_i\to \chi$ and $\gamma_i\cdot\chi_i \to \omega$ in the dual stabilizer groupoid $\widehat{S}$ where the $\gamma_i\in G$ act via conjugation, if $\chi$ and $\omega$ are elements of the same fiber then $\chi = \omega$. 10.1017/S0004972713000129

Published

2013-08-11

Issue

Vol. 88 No. 2 (2013)

Section

Articles
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