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

Higher-rank graphs (ork-graphs) were introduced by Kumjian and Pask to provide combinatorial models for the higher-rank Cuntz–KriegerC*-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 theC*-algebras of these 2-graphs, find criteria under which they are simple and purely infinite, and compute theirK-theory. We find examples whoseC*-algebras satisfy the hypotheses of the classification theorem of Kirchberg and Phillips, but are not isomorphic to theC*-algebras of ordinary directed graphs.