Graph Algebras and Orbit Equivalence

  title={Graph Algebras and Orbit Equivalence},
  author={NATHAN BROWNLOWE and Toke M. Carlsen and Michael F. Whittaker},
We introduce the notion of orbit equivalence of directed graphs, following Matsumoto’s notion of continuous orbit equivalence for topological Markov shifts. We show that two graphs in which every cycle has an exit are orbit equivalent if and only if there is a diagonal-preserving isomorphism between their C∗-algebras. We show that it is necessary to assume that every cycle has an exit for the forward implication, but that the reverse implication holds for arbitrary graphs. As part of our… CONTINUE READING

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