Document Type
Journal Article
RIS ID
17456
Citation
Kumjian, Alexander and Pask, David, 2003, Actions of Z^k associated to higher rank graphs, Ergodic Theory and Dynamical Systems, 23(4), 1153-1172.
http://ro.uow.edu.au/era/318
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.
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