@misc{10498/20604,
year = {2018},
month = {6},
url = {http://hdl.handle.net/10498/20604},
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 Z_2 is not simple.},
organization = {The first named author was partially supported by Marsden grant 15-UOO-071 from the Royal Society
of New Zealand. The second named author was partially supported by CNPq. The third named author was partially supported by PAI III grant FQM-298 of the Junta de Andaluc ́ıa, and by the DGI-MINECO and European Regional Development Fund, jointly, through grants MTM2014-53644-P and MTM2017- 83487-P. The fourth named author was partially supported by the Australian Research Council grant DP150101595. The fifth named author was partially supported by a Carleton University internal research grant.},
publisher = {arXiv},
keywords = {Groupoid C*-algebra},
keywords = {Steinberg algebra},
keywords = {Self-similar graph algebra},
title = {Simplicity of algebras associated to non-hausdorff groupoids},
doi = {10.1090/tran/7840},
author = {Clark, Lisa Orloff and Exel, Ruy and Pardo Espino, Enrique and Sims, Aidan and Starling, Charles},
}