Actions of ${\mathbb Z}^k$ associated to higher rnak graphs
Abstract
Description
An action of ${\mathbb Z}^k$ 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.
Sixteen pages with no figures. To appear Ergodic Theory and Dynamical Systems
Sixteen pages with no figures. To appear Ergodic Theory and Dynamical Systems