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

  • ALEX KUMJIAN (a1) and DAVID PASK (a2)

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.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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