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arXiv · 1806.04362

Simplicity of algebras associated to non-Hausdorff groupoids

Lisa Orloff Clark·Ruy Exel·Enrique Pardo·Aidan Sims·Charles Starling
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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 \'etale 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 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 $\mathbb{Z}_2$ is not simple.

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Lisa Orloff Clark, Ruy Exel, Enrique Pardo, Aidan Sims, Charles Starling. 2018-06-12. Simplicity of algebras associated to non-Hausdorff groupoids. https://arxiv.org/abs/1806.04362

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