We're sorry but this page doesn't work properly without JavaScript enabled. Please enable it to continue.
Feedback

Simplicity of algebras associated to non-Hausdorff groupoids

Formal Metadata

Title
Simplicity of algebras associated to non-Hausdorff groupoids
Title of Series
Number of Parts
11
Author
License
CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
Identifiers
Publisher
Release Date
Language

Content Metadata

Subject Area
Genre
Abstract
We give conditions on a potentially non-Hausdorff étale groupoid which guarantee that its associated C*-algebra is simple. As a key source of examples, work of Nekrashevych and Exel-Pardo describes a class of C*-algebras arising from the action of a group on a finite alphabet (or more generally, a finite graph). The above authors described these as groupoid C*-algebras and gave conditions which guaranteed their simplicity, usually starting from assumptions which imply the groupoid is Hausdorff. These groupoids need not be Hausdorff, notably for the self-similar action associated to the Grigorchuk group, so it was an open question whether the C*-algebra of the Grigorchuk group action was simple or not. We answer this question in the affirmative. We also discuss simplicity criteria for the associated Steinberg algebras.