On the Tits-Weiss conjecture and the Kneser-Tits conjecture for E_78^ 7,1 and E_78^8,2 (With an Appendix by R. M. Weiss)

Autores
Alsaody, Seidon; Chernousov, Vladimir; Pianzola, Arturo
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove that the structure group of any Albert algebra over an arbitrary field is R-trivial. This implies the Tits-Weiss conjecture for Albert algebras and the Kneser-Tits conjecture for isotropic groups of type E78 7,1 and E78 8,2. As a further corollary, we show that some standard conjectures on the groups of R-equivalence classes in algebraic groups and the norm principle are true for strongly inner forms of type 1E6.
Fil: Alsaody, Seidon. Uppsala Universitet.; Suecia
Fil: Chernousov, Vladimir. University of Alberta; Canadá
Fil: Pianzola, Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Centro de Altos Estudios en Ciencias Exactas; Argentina. University of Alberta; Canadá
Materia
Tits-Weiss Conjecture
Kneser-Tits
Albert Algebras
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:11336/166211
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/166211
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On the Tits-Weiss conjecture and the Kneser-Tits conjecture for E_78^ 7,1 and E_78^8,2 (With an Appendix by R. M. Weiss)Alsaody, SeidonChernousov, VladimirPianzola, ArturoTits-Weiss ConjectureKneser-TitsAlbert Algebrashttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove that the structure group of any Albert algebra over an arbitrary field is R-trivial. This implies the Tits-Weiss conjecture for Albert algebras and the Kneser-Tits conjecture for isotropic groups of type E78 7,1 and E78 8,2. As a further corollary, we show that some standard conjectures on the groups of R-equivalence classes in algebraic groups and the norm principle are true for strongly inner forms of type 1E6.Fil: Alsaody, Seidon. Uppsala Universitet.; SueciaFil: Chernousov, Vladimir. University of Alberta; CanadáFil: Pianzola, Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Centro de Altos Estudios en Ciencias Exactas; Argentina. University of Alberta; CanadáCambridge University Press2021-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/166211Alsaody, Seidon; Chernousov, Vladimir; Pianzola, Arturo; On the Tits-Weiss conjecture and the Kneser-Tits conjecture for E_78^ 7,1 and E_78^8,2 (With an Appendix by R. M. Weiss); Cambridge University Press; Forum of Mathematics, Sigma; 9; e75; 11-2021; 1-252050-5094CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/forum-of-mathematics-sigma/article/on-the-titsweiss-conjecture-and-the-knesertits-conjecture-for-mathrm-e7871-and-mathrm-e7882-with-an-appendix-by-r-m-weiss/BA96C697C833167A625F0FEC545AB93Ainfo:eu-repo/semantics/altIdentifier/doi/10.1017/fms.2021.65info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:03:48Zoai:ri.conicet.gov.ar:11336/166211instacron: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 10:03:49.068CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the Tits-Weiss conjecture and the Kneser-Tits conjecture for E_78^ 7,1 and E_78^8,2 (With an Appendix by R. M. Weiss)
title On the Tits-Weiss conjecture and the Kneser-Tits conjecture for E_78^ 7,1 and E_78^8,2 (With an Appendix by R. M. Weiss)
spellingShingle On the Tits-Weiss conjecture and the Kneser-Tits conjecture for E_78^ 7,1 and E_78^8,2 (With an Appendix by R. M. Weiss)
Alsaody, Seidon
Tits-Weiss Conjecture
Kneser-Tits
Albert Algebras
title_short On the Tits-Weiss conjecture and the Kneser-Tits conjecture for E_78^ 7,1 and E_78^8,2 (With an Appendix by R. M. Weiss)
title_full On the Tits-Weiss conjecture and the Kneser-Tits conjecture for E_78^ 7,1 and E_78^8,2 (With an Appendix by R. M. Weiss)
title_fullStr On the Tits-Weiss conjecture and the Kneser-Tits conjecture for E_78^ 7,1 and E_78^8,2 (With an Appendix by R. M. Weiss)
title_full_unstemmed On the Tits-Weiss conjecture and the Kneser-Tits conjecture for E_78^ 7,1 and E_78^8,2 (With an Appendix by R. M. Weiss)
title_sort On the Tits-Weiss conjecture and the Kneser-Tits conjecture for E_78^ 7,1 and E_78^8,2 (With an Appendix by R. M. Weiss)
dc.creator.none.fl_str_mv Alsaody, Seidon
Chernousov, Vladimir
Pianzola, Arturo
author Alsaody, Seidon
author_facet Alsaody, Seidon
Chernousov, Vladimir
Pianzola, Arturo
author_role author
author2 Chernousov, Vladimir
Pianzola, Arturo
author2_role author
author
dc.subject.none.fl_str_mv Tits-Weiss Conjecture
Kneser-Tits
Albert Algebras
topic Tits-Weiss Conjecture
Kneser-Tits
Albert Algebras
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 the structure group of any Albert algebra over an arbitrary field is R-trivial. This implies the Tits-Weiss conjecture for Albert algebras and the Kneser-Tits conjecture for isotropic groups of type E78 7,1 and E78 8,2. As a further corollary, we show that some standard conjectures on the groups of R-equivalence classes in algebraic groups and the norm principle are true for strongly inner forms of type 1E6.
Fil: Alsaody, Seidon. Uppsala Universitet.; Suecia
Fil: Chernousov, Vladimir. University of Alberta; Canadá
Fil: Pianzola, Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Centro de Altos Estudios en Ciencias Exactas; Argentina. University of Alberta; Canadá
description We prove that the structure group of any Albert algebra over an arbitrary field is R-trivial. This implies the Tits-Weiss conjecture for Albert algebras and the Kneser-Tits conjecture for isotropic groups of type E78 7,1 and E78 8,2. As a further corollary, we show that some standard conjectures on the groups of R-equivalence classes in algebraic groups and the norm principle are true for strongly inner forms of type 1E6.
publishDate 2021
dc.date.none.fl_str_mv 2021-11
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/11336/166211
Alsaody, Seidon; Chernousov, Vladimir; Pianzola, Arturo; On the Tits-Weiss conjecture and the Kneser-Tits conjecture for E_78^ 7,1 and E_78^8,2 (With an Appendix by R. M. Weiss); Cambridge University Press; Forum of Mathematics, Sigma; 9; e75; 11-2021; 1-25
2050-5094
CONICET Digital
CONICET
url http://hdl.handle.net/11336/166211
identifier_str_mv Alsaody, Seidon; Chernousov, Vladimir; Pianzola, Arturo; On the Tits-Weiss conjecture and the Kneser-Tits conjecture for E_78^ 7,1 and E_78^8,2 (With an Appendix by R. M. Weiss); Cambridge University Press; Forum of Mathematics, Sigma; 9; e75; 11-2021; 1-25
2050-5094
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.cambridge.org/core/journals/forum-of-mathematics-sigma/article/on-the-titsweiss-conjecture-and-the-knesertits-conjecture-for-mathrm-e7871-and-mathrm-e7882-with-an-appendix-by-r-m-weiss/BA96C697C833167A625F0FEC545AB93A
info:eu-repo/semantics/altIdentifier/doi/10.1017/fms.2021.65
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
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
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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