Journal of Operator Theory

Volume 57, Issue 1, Winter 2007 pp. 207-226.

$C^*$-algebras of labelled graphs

Authors: Teresa Bates (1) and David Pask (2)
Author institution: (1) School of Mathematics and Statistics, UNSW, Sydney 2052, Australia
(2) School of Mathematical and Physical Sciences, The University of Newcastle, NSW 2308, Australia

Summary: 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.

Keywords: $C^*$-algebras, labelled graph, ultragraph, shift space, Matsumoto algebra.

Contents Full-Text PDF