Asymptotic C∗-Algebras from ℤk-Actions on Higher Rank Graphs

Abstract EN

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.