2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159322Higher-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.28 pages, 3 figures, 1 tableOperator AlgebrasDynamical Systems46L05; 37B50text