The classification problem for von Neumann factors

Autores
Sasyk, Roman; Törnquist, Asger
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove that it is not possible to classify separable von Neumann factors of types II1, II∞ or IIIλ, 0 λ 1, up to isomorphism by a Borel measurable assignment of “countable structures” as invariants. In particular the isomorphism relation of type II1 factors is not smooth. We also prove that the isomorphism relation for von Neumann II1 factors is analytic, but is not Borel.
Fil: Sasyk, Roman. University of Ottawa; Canadá. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Fil: Törnquist, Asger. University of Toronto; Canadá
Materia
von Neumann algebras
Classification
Borel reducibility
Turbulence
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:11336/19477
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The classification problem for von Neumann factorsSasyk, RomanTörnquist, Asgervon Neumann algebrasClassificationBorel reducibilityTurbulencehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove that it is not possible to classify separable von Neumann factors of types II1, II∞ or IIIλ, 0 λ 1, up to isomorphism by a Borel measurable assignment of “countable structures” as invariants. In particular the isomorphism relation of type II1 factors is not smooth. We also prove that the isomorphism relation for von Neumann II1 factors is analytic, but is not Borel.Fil: Sasyk, Roman. University of Ottawa; Canadá. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaFil: Törnquist, Asger. University of Toronto; CanadáElsevier2008-12info: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/11336/19477Sasyk, Roman; Törnquist, Asger; The classification problem for von Neumann factors; Elsevier; Journal Of Functional Analysis; 256; 8; 12-2008; 2710-27240022-1236CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022123608005028info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jfa.2008.11.010info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:02:50Zoai:ri.conicet.gov.ar:11336/19477instacron: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:34982025-09-10 13:02:50.299CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The classification problem for von Neumann factors
title The classification problem for von Neumann factors
spellingShingle The classification problem for von Neumann factors
Sasyk, Roman
von Neumann algebras
Classification
Borel reducibility
Turbulence
title_short The classification problem for von Neumann factors
title_full The classification problem for von Neumann factors
title_fullStr The classification problem for von Neumann factors
title_full_unstemmed The classification problem for von Neumann factors
title_sort The classification problem for von Neumann factors
dc.creator.none.fl_str_mv Sasyk, Roman
Törnquist, Asger
author Sasyk, Roman
author_facet Sasyk, Roman
Törnquist, Asger
author_role author
author2 Törnquist, Asger
author2_role author
dc.subject.none.fl_str_mv von Neumann algebras
Classification
Borel reducibility
Turbulence
topic von Neumann algebras
Classification
Borel reducibility
Turbulence
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 that it is not possible to classify separable von Neumann factors of types II1, II∞ or IIIλ, 0 λ 1, up to isomorphism by a Borel measurable assignment of “countable structures” as invariants. In particular the isomorphism relation of type II1 factors is not smooth. We also prove that the isomorphism relation for von Neumann II1 factors is analytic, but is not Borel.
Fil: Sasyk, Roman. University of Ottawa; Canadá. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Fil: Törnquist, Asger. University of Toronto; Canadá
description We prove that it is not possible to classify separable von Neumann factors of types II1, II∞ or IIIλ, 0 λ 1, up to isomorphism by a Borel measurable assignment of “countable structures” as invariants. In particular the isomorphism relation of type II1 factors is not smooth. We also prove that the isomorphism relation for von Neumann II1 factors is analytic, but is not Borel.
publishDate 2008
dc.date.none.fl_str_mv 2008-12
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/11336/19477
Sasyk, Roman; Törnquist, Asger; The classification problem for von Neumann factors; Elsevier; Journal Of Functional Analysis; 256; 8; 12-2008; 2710-2724
0022-1236
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19477
identifier_str_mv Sasyk, Roman; Törnquist, Asger; The classification problem for von Neumann factors; Elsevier; Journal Of Functional Analysis; 256; 8; 12-2008; 2710-2724
0022-1236
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022123608005028
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jfa.2008.11.010
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 Elsevier
publisher.none.fl_str_mv Elsevier
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 12.993085

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