Simplicity of twisted C*-algebras of Deaconu–Renault groupoids

Authors

Becky Armstrong, Victoria University of Wellington
Nathan Brownlowe, The University of Sydney
Aidan Sims, University of Wollongong

Publication Name

Journal of Noncommutative Geometry

Abstract

We consider Deaconu–Renault groupoids associated to actions of finite-rank free abelian monoids by local homeomorphisms of locally compact Hausdorff spaces. We study simplicity of the twisted C*-algebra of such a groupoid determined by a continuous circle-valued groupoid 2-cocycle. When the groupoid is not minimal, this C*-algebra is never simple, so we focus on minimal groupoids. We describe an action of the quotient of the groupoid by the interior of its isotropy on the spectrum of the twisted C*-algebra of the interior of the isotropy. We prove that the twisted groupoid C*-algebra is simple if and only if this action is minimal. We describe applications to crossed products of topological-graph C*-algebras by quasi-free actions.

Open Access Status

This publication may be available as open access

Volume

18

Issue

1

First Page

265

Last Page

312

Funding Number

DP200100155

Funding Sponsor

Australian Research Council