Actions of Z^k associated to higher rank graphs

Date: 
Thu, Aug 1, 2002
Author: 
U. Kumjian,
D. Pask
Location: 
University of Victoria, Victoria, Canada
Conference: 
Aperiodic Order, Dynamical Systems, Operator Algebras and Topology
Abstract: 
We construct an action of $\mathbb Z^k$ on a compact zero-dimensional space obtained from a higher graph $\Lambda$ satisfying a mild assumption generalizing the construction of the Markov shift associated to a nonnegative integer matrix. The stable Ruelle algebra $R_s(\Lambda)$ is shown to be strongly Morita equivalent to $C^*(\Lambda)$. Hence $R_s(\Lambda)$ is simple, stable and purely infinite, if $\Lambda$ satisfies the aperiodicity condition.

Published in: Ergodic Theory Dynam. Systems 23 (2003), no. 4, 1153-1172.

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