Building on recent work of Robertson and Steger, we associate a C∗–algebra to a combinatorial object which may be thought of as higher rank graph. This C∗–algebra is shown to be isomorphic to that of the associated path groupoid. Sufficient conditions on the higher rank graph are found for the associated C∗–algebra to be simple, purely infinite and AF. Results concerning the structure of crossed products by certain natural actions of discrete groups are obtained; a technique for constructing… CONTINUE READING