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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/752497 |
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| _version_ | 1832562096357769216 |
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| author | Inhyeop Yi |
| author_facet | Inhyeop Yi |
| author_sort | Inhyeop Yi |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-0eb3d065632747948367273e1b9d00f0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0eb3d065632747948367273e1b9d00f02025-02-03T01:23:23ZengWileyAbstract 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 |
| spellingShingle | Inhyeop Yi Asymptotic -Algebras from -Actions on Higher Rank Graphs Abstract and Applied Analysis |
| title | 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_short | Asymptotic -Algebras from -Actions on Higher Rank Graphs |
| title_sort | asymptotic algebras from actions on higher rank graphs |
| url | http://dx.doi.org/10.1155/2013/752497 |
| work_keys_str_mv | AT inhyeopyi asymptoticalgebrasfromactionsonhigherrankgraphs |