Algebraic bivariant K-theory and Leavitt path algebras

Autores
Cortiñas, Guillermo Horacio; Montero, Diego
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We investigate to what extent homotopy invariant, excisive and matrix stable homology theories help one distinguish between the Leavitt path algebras L.E/ and L.F / of graphs E and F over a commutative ground ring `. We approach this by studying the structure of such algebras under bivariant algebraic K-theory kk, which is the universal homology theory with the properties above. We show that under very mild assumptions on `, for a graph E with finitely many vertices and reduced incidence matrix AE, the structure of L.E/ in kk depends only on the groups Coker.I AE/ and Coker.I A t E/. We also prove that for Leavitt path algebras, kk has several properties similar to those that Kasparov’s bivariant K-theory has for C -graph algebras, including analogues of the Universal coefficient and Künneth theorems of Rosenberg and Schochet
Fil: Cortiñas, Guillermo Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Montero, Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
Leavitt path algebras
Classification
Algebraic bivariant K-theory
Universal coefficient theorem
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/161955
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Algebraic bivariant K-theory and Leavitt path algebrasCortiñas, Guillermo HoracioMontero, DiegoLeavitt path algebrasClassificationAlgebraic bivariant K-theoryUniversal coefficient theoremhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We investigate to what extent homotopy invariant, excisive and matrix stable homology theories help one distinguish between the Leavitt path algebras L.E/ and L.F / of graphs E and F over a commutative ground ring `. We approach this by studying the structure of such algebras under bivariant algebraic K-theory kk, which is the universal homology theory with the properties above. We show that under very mild assumptions on `, for a graph E with finitely many vertices and reduced incidence matrix AE, the structure of L.E/ in kk depends only on the groups Coker.I AE/ and Coker.I A t E/. We also prove that for Leavitt path algebras, kk has several properties similar to those that Kasparov’s bivariant K-theory has for C -graph algebras, including analogues of the Universal coefficient and Künneth theorems of Rosenberg and SchochetFil: Cortiñas, Guillermo Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Montero, Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaEuropean Mathematical Society2021-02-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/161955Cortiñas, Guillermo Horacio; Montero, Diego; Algebraic bivariant K-theory and Leavitt path algebras; European Mathematical Society; Journal of Noncommutative Geometry; 25; 1; 2-2-2021; 113-1461661-69521661-6960CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.4171/jncg/397info:eu-repo/semantics/altIdentifier/url/https://ems.press/journals/jncg/articles/17454info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:34:47Zoai:ri.conicet.gov.ar:11336/161955instacron: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:34982025-11-12 09:34:47.962CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Algebraic bivariant K-theory and Leavitt path algebras
title Algebraic bivariant K-theory and Leavitt path algebras
spellingShingle Algebraic bivariant K-theory and Leavitt path algebras
Cortiñas, Guillermo Horacio
Leavitt path algebras
Classification
Algebraic bivariant K-theory
Universal coefficient theorem
title_short Algebraic bivariant K-theory and Leavitt path algebras
title_full Algebraic bivariant K-theory and Leavitt path algebras
title_fullStr Algebraic bivariant K-theory and Leavitt path algebras
title_full_unstemmed Algebraic bivariant K-theory and Leavitt path algebras
title_sort Algebraic bivariant K-theory and Leavitt path algebras
dc.creator.none.fl_str_mv Cortiñas, Guillermo Horacio
Montero, Diego
author Cortiñas, Guillermo Horacio
author_facet Cortiñas, Guillermo Horacio
Montero, Diego
author_role author
author2 Montero, Diego
author2_role author
dc.subject.none.fl_str_mv Leavitt path algebras
Classification
Algebraic bivariant K-theory
Universal coefficient theorem
topic Leavitt path algebras
Classification
Algebraic bivariant K-theory
Universal coefficient theorem
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 investigate to what extent homotopy invariant, excisive and matrix stable homology theories help one distinguish between the Leavitt path algebras L.E/ and L.F / of graphs E and F over a commutative ground ring `. We approach this by studying the structure of such algebras under bivariant algebraic K-theory kk, which is the universal homology theory with the properties above. We show that under very mild assumptions on `, for a graph E with finitely many vertices and reduced incidence matrix AE, the structure of L.E/ in kk depends only on the groups Coker.I AE/ and Coker.I A t E/. We also prove that for Leavitt path algebras, kk has several properties similar to those that Kasparov’s bivariant K-theory has for C -graph algebras, including analogues of the Universal coefficient and Künneth theorems of Rosenberg and Schochet
Fil: Cortiñas, Guillermo Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Montero, Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description We investigate to what extent homotopy invariant, excisive and matrix stable homology theories help one distinguish between the Leavitt path algebras L.E/ and L.F / of graphs E and F over a commutative ground ring `. We approach this by studying the structure of such algebras under bivariant algebraic K-theory kk, which is the universal homology theory with the properties above. We show that under very mild assumptions on `, for a graph E with finitely many vertices and reduced incidence matrix AE, the structure of L.E/ in kk depends only on the groups Coker.I AE/ and Coker.I A t E/. We also prove that for Leavitt path algebras, kk has several properties similar to those that Kasparov’s bivariant K-theory has for C -graph algebras, including analogues of the Universal coefficient and Künneth theorems of Rosenberg and Schochet
publishDate 2021
dc.date.none.fl_str_mv 2021-02-02
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/11336/161955
Cortiñas, Guillermo Horacio; Montero, Diego; Algebraic bivariant K-theory and Leavitt path algebras; European Mathematical Society; Journal of Noncommutative Geometry; 25; 1; 2-2-2021; 113-146
1661-6952
1661-6960
CONICET Digital
CONICET
url http://hdl.handle.net/11336/161955
identifier_str_mv Cortiñas, Guillermo Horacio; Montero, Diego; Algebraic bivariant K-theory and Leavitt path algebras; European Mathematical Society; Journal of Noncommutative Geometry; 25; 1; 2-2-2021; 113-146
1661-6952
1661-6960
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.4171/jncg/397
info:eu-repo/semantics/altIdentifier/url/https://ems.press/journals/jncg/articles/17454
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv European Mathematical Society
publisher.none.fl_str_mv European 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 12.976206

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