Actions of Z^k associated to higher rank graphs

Authors

Alexander Kumjian, University of Nevada
David Pask, University of WollongongFollow

RIS ID

17456

Publication Details

Kumjian, A. & Pask, D. (2003). Actions of Z^k associated to higher rank graphs. Ergodic Theory and Dynamical Systems, 23 (4), 1153-1172.

Abstract

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.