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Actions Of Z^K Associated To Higher Rank Graphs, Alexander Kumjian, David Pask

Faculty of Engineering and Information Sciences - Papers: Part A

An action of Z^k is associated to a higher rank graph Λ satisfying a mild assumption. This generalizes the construction of a topological Markov shift arising from a non-negative integer matrix. We show that the stable Ruelle algebra of Λ is strongly Morita equivalent to C^∗(Λ). Hence, if Λ satisfies the aperiodicity condition, the stable Ruelle algebra is simple, stable and purely infinite.