Purely infinite simple C*-algebras that are principal groupoid C*-algebras

TL;DR

This paper demonstrates how to construct amenable principal groupoids whose C*-algebras are Kirchberg algebras, providing new examples of UCT Kirchberg algebras as groupoid C*-algebras.

Contribution

It introduces a method to realize many UCT Kirchberg algebras as C*-algebras of amenable principal groupoids, linking groupoid theory with Kirchberg algebra classification.

Findings

Constructed amenable principal groupoids with Kirchberg algebra C*-algebras

Showed KK-equivalence between constructed C*-algebras and original groupoid C*-algebras

Provided examples of UCT Kirchberg algebras as groupoid C*-algebras

Abstract

From a suitable groupoid G, we show how to construct an amenable principal groupoid whose C*-algebra is a Kirchberg algebra which is KK-equivalent to C*(G). Using this construction, we show by example that many UCT Kirchberg algebras can be realised as the C*-algebras of amenable principal groupoids.