On C∗-Algebras from Interval Maps
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10174/10099 https://doi.org/10.1007/s11785-011-0132-7 |
Resumo: | Given a unimodal interval map f , we construct partial isometries acting on Hilbert spaces associated to the orbit of each point. Then we prove that such partial isometries give rise to representations of a C∗-algebra associated to the subshift encoding the kneading sequence of the critical point. This construction has the advantage of incorporating maps with a non necessarily Markov partition (e.g. Fibonacci unimodal map). If we are indeed in the presence of a finite Markov partition, then we prove that these new representations coincide with the (previously considered by the authors) representations arising from the Cuntz–Krieger algebra of the underlying (finite) transition matrix. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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On C∗-Algebras from Interval MapsInterval mapsSymbolic dynamicsCuntz–Krieger algebrasRepresentations of algebrasGiven a unimodal interval map f , we construct partial isometries acting on Hilbert spaces associated to the orbit of each point. Then we prove that such partial isometries give rise to representations of a C∗-algebra associated to the subshift encoding the kneading sequence of the critical point. This construction has the advantage of incorporating maps with a non necessarily Markov partition (e.g. Fibonacci unimodal map). If we are indeed in the presence of a finite Markov partition, then we prove that these new representations coincide with the (previously considered by the authors) representations arising from the Cuntz–Krieger algebra of the underlying (finite) transition matrix.Springer Verlag2014-01-27T16:52:28Z2014-01-272013-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10174/10099http://hdl.handle.net/10174/10099https://doi.org/10.1007/s11785-011-0132-7engRamos, C. Correia; Martins, Nuno; Pinto, Paulo R. On C∗-algebras from interval maps. Complex Anal. Oper. Theory 7 (2013), no. 1, 221–235.DMAT, CIMAccr@uevora.pt721Correia Ramos, C.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-03T18:52:37Zoai:dspace.uevora.pt:10174/10099Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:04:03.015506Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
On C∗-Algebras from Interval Maps |
title |
On C∗-Algebras from Interval Maps |
spellingShingle |
On C∗-Algebras from Interval Maps Correia Ramos, C. Interval maps Symbolic dynamics Cuntz–Krieger algebras Representations of algebras |
title_short |
On C∗-Algebras from Interval Maps |
title_full |
On C∗-Algebras from Interval Maps |
title_fullStr |
On C∗-Algebras from Interval Maps |
title_full_unstemmed |
On C∗-Algebras from Interval Maps |
title_sort |
On C∗-Algebras from Interval Maps |
author |
Correia Ramos, C. |
author_facet |
Correia Ramos, C. |
author_role |
author |
dc.contributor.author.fl_str_mv |
Correia Ramos, C. |
dc.subject.por.fl_str_mv |
Interval maps Symbolic dynamics Cuntz–Krieger algebras Representations of algebras |
topic |
Interval maps Symbolic dynamics Cuntz–Krieger algebras Representations of algebras |
description |
Given a unimodal interval map f , we construct partial isometries acting on Hilbert spaces associated to the orbit of each point. Then we prove that such partial isometries give rise to representations of a C∗-algebra associated to the subshift encoding the kneading sequence of the critical point. This construction has the advantage of incorporating maps with a non necessarily Markov partition (e.g. Fibonacci unimodal map). If we are indeed in the presence of a finite Markov partition, then we prove that these new representations coincide with the (previously considered by the authors) representations arising from the Cuntz–Krieger algebra of the underlying (finite) transition matrix. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013-01-01T00:00:00Z 2014-01-27T16:52:28Z 2014-01-27 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10174/10099 http://hdl.handle.net/10174/10099 https://doi.org/10.1007/s11785-011-0132-7 |
url |
http://hdl.handle.net/10174/10099 https://doi.org/10.1007/s11785-011-0132-7 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Ramos, C. Correia; Martins, Nuno; Pinto, Paulo R. On C∗-algebras from interval maps. Complex Anal. Oper. Theory 7 (2013), no. 1, 221–235. DMAT, CIMA ccr@uevora.pt 721 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Springer Verlag |
publisher.none.fl_str_mv |
Springer Verlag |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799136524618432512 |