AsymptoticC∗-Algebras fromℤk-Actions on Higher Rank Graphs

摘要

For a dynamical system arising fromℤk-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 thek-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.