Skip to main content
placeholder image

Simplicity Of Algebras Associated To Non-Hausdorff Groupoids

Journal Article


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 ├ętale 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.

UOW Authors


  •   Clark, Lisa Orloff (external author)
  •   Exel Filho, Ruy (external author)
  •   Pardo, Enrique (external author)
  •   Sims, Aidan
  •   Starling, Charles (external author)

Publication Date


  • 2019

Citation


  • 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.

Scopus Eid


  • 2-s2.0-85072361127

Number Of Pages


  • 43

Start Page


  • 3669

End Page


  • 3712

Volume


  • 372

Issue


  • 5

Place Of Publication


  • United States

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 ├ętale 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.

UOW Authors


  •   Clark, Lisa Orloff (external author)
  •   Exel Filho, Ruy (external author)
  •   Pardo, Enrique (external author)
  •   Sims, Aidan
  •   Starling, Charles (external author)

Publication Date


  • 2019

Citation


  • 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.

Scopus Eid


  • 2-s2.0-85072361127

Number Of Pages


  • 43

Start Page


  • 3669

End Page


  • 3712

Volume


  • 372

Issue


  • 5

Place Of Publication


  • United States