%0 Journal Article 
%A Clark, Lisa Orloff
%A Exel, Ruy
%A Pardo Espino, Enrique
%A Sims, Aidan
%A Starling, Charles
%T Simplicity of algebras associated to non-hausdorff groupoids
%D 2018
%U http://hdl.handle.net/10498/20604
%X 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 Z_2 is not simple.
%K Groupoid C*-algebra
%K Steinberg algebra
%K Self-similar graph algebra
%~ Universidad de Cádiz