Tensor products of Leavitt path algebras

Autores
Ara, Pere; Cortiñas, Guillermo Horacio
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We compute the Hochschild homology of Leavitt path algebras over a field k. As an application, we show that L2 and L2 ⊗ L2 have different Hochschild homologies, and so they are not Morita equivalent; in particular, they are not isomorphic. Similarly, L∞ and L∞ ⊗ L∞ are distinguished by their Hochschild homologies, and so they are not Morita equivalent either. By contrast, we show that K-theory cannot distinguish these algebras; we have K∗(L2) = K∗(L2 ⊗ L2) = 0 and K∗(L∞) = K∗(L∞ ⊗ L∞) = K∗(k).
Fil: Ara, Pere. Universidad de Barcelona; España
Fil: Cortiñas, Guillermo Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "luis A. Santaló"; Argentina
Materia
Leavitt Path Algebras
Cuntz-Krieger Algebras
Hochschild Homology
K-Theory
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/14840
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/14840
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Tensor products of Leavitt path algebrasAra, PereCortiñas, Guillermo HoracioLeavitt Path AlgebrasCuntz-Krieger AlgebrasHochschild HomologyK-Theoryhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We compute the Hochschild homology of Leavitt path algebras over a field k. As an application, we show that L2 and L2 ⊗ L2 have different Hochschild homologies, and so they are not Morita equivalent; in particular, they are not isomorphic. Similarly, L∞ and L∞ ⊗ L∞ are distinguished by their Hochschild homologies, and so they are not Morita equivalent either. By contrast, we show that K-theory cannot distinguish these algebras; we have K∗(L2) = K∗(L2 ⊗ L2) = 0 and K∗(L∞) = K∗(L∞ ⊗ L∞) = K∗(k).Fil: Ara, Pere. Universidad de Barcelona; EspañaFil: Cortiñas, Guillermo Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "luis A. Santaló"; ArgentinaAmerican Mathematical Society2013-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14840Ara, Pere; Cortiñas, Guillermo Horacio; Tensor products of Leavitt path algebras; American Mathematical Society; Proceedings of the American Mathematical Society; 141; 8; 4-2013; 2629-26390002-9939enginfo:eu-repo/semantics/altIdentifier/url/http://dx.doi.org/10.1090/S0002-9939-2013-11561-3info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/proc/2013-141-08/S0002-9939-2013-11561-3/home.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:51:21Zoai:ri.conicet.gov.ar:11336/14840instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:51:21.381CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Tensor products of Leavitt path algebras
title Tensor products of Leavitt path algebras
spellingShingle Tensor products of Leavitt path algebras
Ara, Pere
Leavitt Path Algebras
Cuntz-Krieger Algebras
Hochschild Homology
K-Theory
title_short Tensor products of Leavitt path algebras
title_full Tensor products of Leavitt path algebras
title_fullStr Tensor products of Leavitt path algebras
title_full_unstemmed Tensor products of Leavitt path algebras
title_sort Tensor products of Leavitt path algebras
dc.creator.none.fl_str_mv Ara, Pere
Cortiñas, Guillermo Horacio
author Ara, Pere
author_facet Ara, Pere
Cortiñas, Guillermo Horacio
author_role author
author2 Cortiñas, Guillermo Horacio
author2_role author
dc.subject.none.fl_str_mv Leavitt Path Algebras
Cuntz-Krieger Algebras
Hochschild Homology
K-Theory
topic Leavitt Path Algebras
Cuntz-Krieger Algebras
Hochschild Homology
K-Theory
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We compute the Hochschild homology of Leavitt path algebras over a field k. As an application, we show that L2 and L2 ⊗ L2 have different Hochschild homologies, and so they are not Morita equivalent; in particular, they are not isomorphic. Similarly, L∞ and L∞ ⊗ L∞ are distinguished by their Hochschild homologies, and so they are not Morita equivalent either. By contrast, we show that K-theory cannot distinguish these algebras; we have K∗(L2) = K∗(L2 ⊗ L2) = 0 and K∗(L∞) = K∗(L∞ ⊗ L∞) = K∗(k).
Fil: Ara, Pere. Universidad de Barcelona; España
Fil: Cortiñas, Guillermo Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "luis A. Santaló"; Argentina
description We compute the Hochschild homology of Leavitt path algebras over a field k. As an application, we show that L2 and L2 ⊗ L2 have different Hochschild homologies, and so they are not Morita equivalent; in particular, they are not isomorphic. Similarly, L∞ and L∞ ⊗ L∞ are distinguished by their Hochschild homologies, and so they are not Morita equivalent either. By contrast, we show that K-theory cannot distinguish these algebras; we have K∗(L2) = K∗(L2 ⊗ L2) = 0 and K∗(L∞) = K∗(L∞ ⊗ L∞) = K∗(k).
publishDate 2013
dc.date.none.fl_str_mv 2013-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/14840
Ara, Pere; Cortiñas, Guillermo Horacio; Tensor products of Leavitt path algebras; American Mathematical Society; Proceedings of the American Mathematical Society; 141; 8; 4-2013; 2629-2639
0002-9939
url http://hdl.handle.net/11336/14840
identifier_str_mv Ara, Pere; Cortiñas, Guillermo Horacio; Tensor products of Leavitt path algebras; American Mathematical Society; Proceedings of the American Mathematical Society; 141; 8; 4-2013; 2629-2639
0002-9939
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://dx.doi.org/10.1090/S0002-9939-2013-11561-3
info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/proc/2013-141-08/S0002-9939-2013-11561-3/home.html
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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