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 Λ we consider has an associated C*-algebra, denoted C*(Λ), which is simple and purely infinite when Λ is aperiodic. We give new, straightforward conditions which ensure that Λ is aperiodic. These conditions are highly tractable as we only need to consider the finite set of vertices of Λ 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.