C*-algebras of labelled graphs

Abstract

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