Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space

Autores
Cortiñas, Guillermo Horacio; Tartaglia, Gisela
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove the K-theoretic Farrell-Jones conjecture for groups with the Haagerup approximation property and coefficient rings and C ∗ C^{∗} -algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes conjecture holds for such a group G, to show that the algebraic and the C ∗ C^{∗} -crossed product of G with a stable separable G- C ∗ C^{∗} -algebra have the same K-theory.
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
Fil: Tartaglia, Gisela. 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
Materia
Algebraic K-theory
Stable C*-algebras
Farrell-Jones conjecture
Haagerup groups
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:11336/88996
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert spaceCortiñas, Guillermo HoracioTartaglia, GiselaAlgebraic K-theoryStable C*-algebrasFarrell-Jones conjectureHaagerup groupshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove the K-theoretic Farrell-Jones conjecture for groups with the Haagerup approximation property and coefficient rings and C ∗ C^{∗} -algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes conjecture holds for such a group G, to show that the algebraic and the C ∗ C^{∗} -crossed product of G with a stable separable G- C ∗ C^{∗} -algebra have the same K-theory.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"; ArgentinaFil: Tartaglia, Gisela. 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"; ArgentinaDe Gruyter2018-01info: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/11336/88996Cortiñas, Guillermo Horacio; Tartaglia, Gisela; Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space; De Gruyter; Journal Fur Die Reine Und Angewandte Mathematik; 2018; 734; 1-2018; 265-2920075-4102CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/crelle.2018.2018.issue-734/crelle-2014-0154/crelle-2014-0154.xmlinfo:eu-repo/semantics/altIdentifier/doi/10.1515/crelle-2014-0154info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:51:08Zoai:ri.conicet.gov.ar:11336/88996instacron: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 09:51:08.665CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space
title Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space
spellingShingle Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space
Cortiñas, Guillermo Horacio
Algebraic K-theory
Stable C*-algebras
Farrell-Jones conjecture
Haagerup groups
title_short Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space
title_full Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space
title_fullStr Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space
title_full_unstemmed Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space
title_sort Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space
dc.creator.none.fl_str_mv Cortiñas, Guillermo Horacio
Tartaglia, Gisela
author Cortiñas, Guillermo Horacio
author_facet Cortiñas, Guillermo Horacio
Tartaglia, Gisela
author_role author
author2 Tartaglia, Gisela
author2_role author
dc.subject.none.fl_str_mv Algebraic K-theory
Stable C*-algebras
Farrell-Jones conjecture
Haagerup groups
topic Algebraic K-theory
Stable C*-algebras
Farrell-Jones conjecture
Haagerup groups
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 prove the K-theoretic Farrell-Jones conjecture for groups with the Haagerup approximation property and coefficient rings and C ∗ C^{∗} -algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes conjecture holds for such a group G, to show that the algebraic and the C ∗ C^{∗} -crossed product of G with a stable separable G- C ∗ C^{∗} -algebra have the same K-theory.
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
Fil: Tartaglia, Gisela. 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
description We prove the K-theoretic Farrell-Jones conjecture for groups with the Haagerup approximation property and coefficient rings and C ∗ C^{∗} -algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes conjecture holds for such a group G, to show that the algebraic and the C ∗ C^{∗} -crossed product of G with a stable separable G- C ∗ C^{∗} -algebra have the same K-theory.
publishDate 2018
dc.date.none.fl_str_mv 2018-01
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/11336/88996
Cortiñas, Guillermo Horacio; Tartaglia, Gisela; Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space; De Gruyter; Journal Fur Die Reine Und Angewandte Mathematik; 2018; 734; 1-2018; 265-292
0075-4102
CONICET Digital
CONICET
url http://hdl.handle.net/11336/88996
identifier_str_mv Cortiñas, Guillermo Horacio; Tartaglia, Gisela; Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space; De Gruyter; Journal Fur Die Reine Und Angewandte Mathematik; 2018; 734; 1-2018; 265-292
0075-4102
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/crelle.2018.2018.issue-734/crelle-2014-0154/crelle-2014-0154.xml
info:eu-repo/semantics/altIdentifier/doi/10.1515/crelle-2014-0154
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
application/pdf
dc.publisher.none.fl_str_mv De Gruyter
publisher.none.fl_str_mv De Gruyter
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 13.25334

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