C*-algebras of labelled graphs II - Simplicity results

TL;DR

This paper establishes conditions for simplicity and pure infiniteness in a broad class of labelled graph C*-algebras, expanding the known classes beyond traditional graph C*-algebras.

Contribution

It introduces new simplicity and pure infiniteness results for labelled graph C*-algebras, demonstrating they encompass a larger class than unital graph C*-algebras.

Findings

Proves simplicity and pure infiniteness for certain labelled graph C*-algebras.

Shows the class of unital labelled graph C*-algebras is strictly larger than unital graph C*-algebras.

Provides examples illustrating the broader class of these algebras.

Abstract

We prove simplicity and pure infiniteness results for a certain class of labelled graph $C^*$-algebras. We show, by example, that this class of unital labelled graph $C^*$-algebras is strictly larger than the class of unital graph $C^*$-algebras.