Actions of Z^k associated to higher rank graphs

Submitted by Gotay on Thu, 2011-04-14 12:42
Author: 
U. Kumjian,
D. Pask
Date: 
Thu, Aug 1, 2002
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.

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