Asymptotic -Algebras from -Actions on Higher Rank Graphs

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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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
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spelling doaj-0eb3d065632747948367273e1b9d00f02020-11-24T22:50:16ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/752497752497Asymptotic -Algebras from -Actions on Higher Rank GraphsInhyeop Yi0Department of Mathematics Education, Ewha Womans University, Seoul 120-750, Republic of KoreaFor 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.http://dx.doi.org/10.1155/2013/752497
collection DOAJ
language English
format Article
sources DOAJ
author Inhyeop Yi
spellingShingle Inhyeop Yi
Asymptotic -Algebras from -Actions on Higher Rank Graphs
Abstract and Applied Analysis
author_facet Inhyeop Yi
author_sort Inhyeop Yi
title Asymptotic -Algebras from -Actions on Higher Rank Graphs
title_short Asymptotic -Algebras from -Actions on Higher Rank Graphs
title_full Asymptotic -Algebras from -Actions on Higher Rank Graphs
title_fullStr Asymptotic -Algebras from -Actions on Higher Rank Graphs
title_full_unstemmed Asymptotic -Algebras from -Actions on Higher Rank Graphs
title_sort asymptotic -algebras from -actions on higher rank graphs
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description 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.
url http://dx.doi.org/10.1155/2013/752497
work_keys_str_mv AT inhyeopyi asymptoticalgebrasfromactionsonhigherrankgraphs
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