For a dynamical system arising from -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 -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.
"Asymptotic -Algebras from -Actions on Higher Rank Graphs." Abstr. Appl. Anal. 2013 (SI20) 1 - 5, 2013. https://doi.org/10.1155/2013/752497