Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-08T05:37:34.764Z Has data issue: false hasContentIssue false

Actions of $\mathbb{Z}^k$ associated to higher rank graphs

Published online by Cambridge University Press:  01 August 2003

ALEX KUMJIAN
Affiliation:
Department of Mathematics, University of Nevada, Reno, NV 89557, USA (e-mail: [email protected])
DAVID PASK
Affiliation:
Mathematics, SMPS, The University of Newcastle, NSW 2308, Australia (e-mail: [email protected])

Abstract

An action of $\mathbb{Z}^k$ is associated to a higher rank graph $\Lambda$ 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 $\Lambda$ is strongly Morita equivalent to $C^*(\Lambda)$. Hence, if $\Lambda$ satisfies the aperiodicity condition, the stable Ruelle algebra is simple, stable and purely infinite.

Type
Research Article
Copyright
2003 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)