Ergodic Theory and Dynamical Systems

Research Article

A family of 2-graphs arising from two-dimensional subshifts

DAVID PASKa1, IAIN RAEBURNa1 and NATASHA A. WEAVERa2

a1 School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia (email: dpask@uow.edu.au, raeburn@uow.edu.au)

a2 School of Mathematical and Physical Sciences, University of Newcastle, NSW 2308, Australia (email: Natasha.Weaver@studentmail.newcastle.edu.au)

Abstract

Higher-rank graphs (or k-graphs) were introduced by Kumjian and Pask to provide combinatorial models for the higher-rank Cuntz–Krieger C*-algebras of Robertson and Steger. Here we consider a family of finite 2-graphs whose path spaces are dynamical systems of algebraic origin, as studied by Schmidt and others. We analyse the C*-algebras of these 2-graphs, find criteria under which they are simple and purely infinite, and compute their K-theory. We find examples whose C*-algebras satisfy the hypotheses of the classification theorem of Kirchberg and Phillips, but are not isomorphic to the C*-algebras of ordinary directed graphs.

(Received April 22 2008)

(Revised September 05 2008)