Actions of Zᵏ associated to higher rnak graphs

الأصل · EN

An action of Zᵏ is associated to a higher rank graph Λ satisfying a mild assumption. This generalises the construction of a topological Markov shift arising from a nonnegative 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.