C*-algebras of labelled graphs

TL;DR

This paper introduces a new class of C*-algebras that generalize existing ultragraph and shift space C*-algebras, providing insights into their relationships and constructing simple C*-algebras for irreducible sofic shifts.

Contribution

It defines a unified framework for C*-algebras of labelled graphs, extending previous models and linking shift space dynamics with operator algebras.

Findings

Unified description of C*-algebras for labelled graphs

Connection between shift spaces and C*-algebra structures

Construction of simple C*-algebras for irreducible sofic shifts

Abstract

We describe a class of $C^*$-algebras which simultaneously generalise the ultragraph algebras of Tomforde and the shift space $C^*$-algebras of Matsumoto. In doing so we shed some new light on the different $C^*$-algebras that may be associated to a shift space. Finally, we show how to associate a simple $C^*$-algebra to an irreducible sofic shift.