Simplicity of algebras associated to étale groupoids

Authors

Jonathan Brown, Kansas State University
Lisa Orloff Clark, University of Otago
Cynthia Farthing, University of Iowa
Aidan Sims, University of WollongongFollow

RIS ID

89218

Publication Details

Brown, J., Clark, L., Farthing, C. & Sims, A. (2014). Simplicity of algebras associated to étale groupoids. Semigroup Forum, 88 (2), 433-452.

Abstract

We prove that the full C*-algebra of a second-countable, Hausdorff, etale, amenable groupoid is simple if and only if the groupoid is both topologically principal and minimal. We also show that if G has totally disconnected unit space, then the complex *-algebra of its inverse semigroup of compact open bisections, as introduced by Steinberg, is simple if and only if G is both effective and minimal.