On the diagonalization of the Ricci flow on Lie groups

Autores
Lauret, Jorge Ruben; Will, Cynthia Eugenia
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The main purpose of this note is to prove that any basis of a nilpotent Lie algebra for which all diagonal left-invariant metrics have diagonal Ricci tensor necessarily produce quite a simple set of structural constants; namely, the bracket of any pair of elements of the basis must be a multiple of one of them and only the bracket of disjoint pairs can be nonzero multiples of the same element. Some applications to the Ricci flow of left-invariant metrics on Lie groups concerning diagonalization are also given.
Fil: Lauret, Jorge Ruben. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Will, Cynthia Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
Ricci Flow
Lie group
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:11336/200759
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/200759
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling On the diagonalization of the Ricci flow on Lie groupsLauret, Jorge RubenWill, Cynthia EugeniaRicci FlowLie grouphttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The main purpose of this note is to prove that any basis of a nilpotent Lie algebra for which all diagonal left-invariant metrics have diagonal Ricci tensor necessarily produce quite a simple set of structural constants; namely, the bracket of any pair of elements of the basis must be a multiple of one of them and only the bracket of disjoint pairs can be nonzero multiples of the same element. Some applications to the Ricci flow of left-invariant metrics on Lie groups concerning diagonalization are also given.Fil: Lauret, Jorge Ruben. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Will, Cynthia Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaAmerican Mathematical Society2012-06info: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/11336/200759Lauret, Jorge Ruben; Will, Cynthia Eugenia; On the diagonalization of the Ricci flow on Lie groups; American Mathematical Society; Proceedings of the American Mathematical Society; 141; 10; 6-2012; 3651-36630002-99391088-6826CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.jstor.org/stable/23562388info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1110.4003info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.1110.4003info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:04:18Zoai:ri.conicet.gov.ar:11336/200759instacron: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:34982025-09-29 10:04:18.373CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the diagonalization of the Ricci flow on Lie groups
title On the diagonalization of the Ricci flow on Lie groups
spellingShingle On the diagonalization of the Ricci flow on Lie groups
Lauret, Jorge Ruben
Ricci Flow
Lie group
title_short On the diagonalization of the Ricci flow on Lie groups
title_full On the diagonalization of the Ricci flow on Lie groups
title_fullStr On the diagonalization of the Ricci flow on Lie groups
title_full_unstemmed On the diagonalization of the Ricci flow on Lie groups
title_sort On the diagonalization of the Ricci flow on Lie groups
dc.creator.none.fl_str_mv Lauret, Jorge Ruben
Will, Cynthia Eugenia
author Lauret, Jorge Ruben
author_facet Lauret, Jorge Ruben
Will, Cynthia Eugenia
author_role author
author2 Will, Cynthia Eugenia
author2_role author
dc.subject.none.fl_str_mv Ricci Flow
Lie group
topic Ricci Flow
Lie group
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The main purpose of this note is to prove that any basis of a nilpotent Lie algebra for which all diagonal left-invariant metrics have diagonal Ricci tensor necessarily produce quite a simple set of structural constants; namely, the bracket of any pair of elements of the basis must be a multiple of one of them and only the bracket of disjoint pairs can be nonzero multiples of the same element. Some applications to the Ricci flow of left-invariant metrics on Lie groups concerning diagonalization are also given.
Fil: Lauret, Jorge Ruben. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Will, Cynthia Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description The main purpose of this note is to prove that any basis of a nilpotent Lie algebra for which all diagonal left-invariant metrics have diagonal Ricci tensor necessarily produce quite a simple set of structural constants; namely, the bracket of any pair of elements of the basis must be a multiple of one of them and only the bracket of disjoint pairs can be nonzero multiples of the same element. Some applications to the Ricci flow of left-invariant metrics on Lie groups concerning diagonalization are also given.
publishDate 2012
dc.date.none.fl_str_mv 2012-06
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/11336/200759
Lauret, Jorge Ruben; Will, Cynthia Eugenia; On the diagonalization of the Ricci flow on Lie groups; American Mathematical Society; Proceedings of the American Mathematical Society; 141; 10; 6-2012; 3651-3663
0002-9939
1088-6826
CONICET Digital
CONICET
url http://hdl.handle.net/11336/200759
identifier_str_mv Lauret, Jorge Ruben; Will, Cynthia Eugenia; On the diagonalization of the Ricci flow on Lie groups; American Mathematical Society; Proceedings of the American Mathematical Society; 141; 10; 6-2012; 3651-3663
0002-9939
1088-6826
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.jstor.org/stable/23562388
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1110.4003
info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.1110.4003
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 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 13.070432

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