Asymptotic -Algebras from -Actions on Higher Rank Graphs

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 asy...

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Bibliographic Details
Main Author: Inhyeop Yi
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/752497
Description
Summary: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.
ISSN:1085-3375
1687-0409