Simplicity Of Algebras Associated To Non-Hausdorff Groupoids

Authors

Lisa Orloff Clark, Victoria University of Wellington
Ruy Exel Filho, Federal University of Santa CatarinaFollow
Enrique Pardo, University of Cadiz
Aidan Sims, University of WollongongFollow
Charles Starling, Carleton University

RIS ID

138088

Publication Details

Clark, L., Exel, R., Pardo, E., Sims, A. & Starling, C. (2019). Simplicity Of Algebras Associated To Non-Hausdorff Groupoids. Transactions Of The American Mathematical Society, 372 (5), 3669-3712.

Abstract

We prove a uniqueness theorem and give a characterization of simplicity for Steinberg algebras associated to non-Hausdorff ample groupoids. We also prove a uniqueness theorem and give a characterization of simplicity for the C*-algebra associated to non-Hausdorff étale groupoids. Then we show how our results apply in the setting of tight representations of inverse semigroups, groups acting on graphs, and self-similar actions. In particular, we show that the C*-algebra and the complex Steinberg algebra of the self-similar action of the Grigorchuk group are simple but the Steinberg algebra with coefficients in Z₂ is not simple.

Grant Number

ARC/DP150101595