RT info:eu-repo/semantics/article
T1 Simplicity of algebras associated to non-hausdorff groupoids
A1 Clark, Lisa Orloff
A1 Exel, Ruy
A1 Pardo, E.
A1 Sims, Aidan
A1 Starling, Charles
A2 Matemáticas
K1 Groupoid C*-algebra
K1 Steinberg algebra
K1 Self-similar graph algebra
AB 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.
PB arXiv
YR 2018
FD 2018-06-12
LK http://hdl.handle.net/10498/20604
UL http://hdl.handle.net/10498/20604
LA eng
NO The first named author was partially supported by Marsden grant 15-UOO-071 from the Royal Societyof 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.
DS Repositorio Institucional de la Universidad de Cádiz
RD 20-oct-2020