Simplicity of groupoid algebras of self-similar groupoids

Josiah Aakre (University of Manchester)

Thursday 19th February 16:00-17:00
Maths 116

Abstract

We will discuss the so-called singular ideal of both the Steinberg algebra and Cuntz-Pimsner C^*-algebra associated to self-similar groupoids. This elusive ideal presented a surprising obstacle to simplicity in the setting of non-Hausdorff topological groupoids. After a light overview of the story so far in the general setting, we will restrict to those algebras built from self-similar groupoids. In the language of inverse semigroup algebras, we show that the search for elements of the singular ideal can be restricted to the self-similar groupoid, and in the case that the action is contracting and the singular ideal is maximal, an algorithm is given which determines whether the Steinberg and C^*-algebras are simple.

Add to your calendar

Download event information as iCalendar file (only this event)