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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 752497, 5 pages
http://dx.doi.org/10.1155/2013/752497
Research Article

Asymptotic -Algebras from -Actions on Higher Rank Graphs

Department of Mathematics Education, Ewha Womans University, Seoul 120-750, Republic of Korea

Received 17 March 2013; Accepted 5 June 2013

Academic Editor: Baodong Zheng

Copyright © 2013 Inhyeop Yi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.