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

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

2001-12-05

arxiv.org/abs/math/0112049v2

Mathematics

Operator Algebras

Sixteen pages with no figures. To appear Ergodic Theory and Dynamical Systems

Scientific paper

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

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