Abstract
For a dynamical system arising from ℤk-action on a higher rank graph with finite vertex set, we show that the semidirect product of the asymptotic equivalence relation groupoid is essentially principal if and only if the k-graph satisfies the aperiodic condition. Then we show that the corresponding asymptotic Ruelle algebra is simple if the graph is primitive with the aperiodic condition.
Original language | English |
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Article number | 752497 |
Journal | Abstract and Applied Analysis |
Volume | 2013 |
DOIs | |
State | Published - 2013 |