Simplicity of 2-Graph Algebras Associated to Dynamical Systems

We give a combinatorial description of a family of 2-graphs which subsumes those described by Pask, Raeburn and Weaver. Each 2-graph A we consider has an associated C*-algebra, denoted C(Lambda), which is simple and purely infinite when Lambda is aperiodic. We give new, straightforward conditions which ensure that Lambda is aperiodic. These conditions are highly tractable as we only need to consider the finite set of vertices of Lambda in order to identify aperiodicity. In addition, the path space of each 2-graph can be realised as a two-dimensional dynamical system which we show must have zero entropy.