The Nash–Moser theorem of Hamilton and rigidity of finite dimensional nilpotent Lie algebras

Autores
Brega, Alfredo Oscar; Cagliero, Leandro Roberto; Chaves Ochoa, Augusto Enrique
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We apply the Nash–Moser theorem for exact sequences of R. Hamilton to the context of deformations of Lie algebras and we discuss some aspects of the scope of this theorem in connection with the polynomial ideal associated to the variety of nilpotent Lie algebras. This allows us to introduce the space Hk-nil 2(g,g), and certain subspaces of it, that provide fine information about the deformations of g in the variety of k-step nilpotent Lie algebras. Then we focus on degenerations and rigidity in the variety of k-step nilpotent Lie algebras of dimension n with n≤7 and, in particular, we obtain rigid Lie algebras and rigid curves in the variety of 3-step nilpotent Lie algebras of dimension 7. We also recover some known results and point out a possible error in a published article related to this subject.
Fil: Brega, Alfredo Oscar. 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: Cagliero, Leandro Roberto. 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: Chaves Ochoa, Augusto Enrique. 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
deformations and rigidity Lie algebras
Cohomology of Lie algebras
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:11336/59986
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/59986
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network_name_str CONICET Digital (CONICET)
spelling The Nash–Moser theorem of Hamilton and rigidity of finite dimensional nilpotent Lie algebrasBrega, Alfredo OscarCagliero, Leandro RobertoChaves Ochoa, Augusto Enriquedeformations and rigidity Lie algebrasCohomology of Lie algebrashttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We apply the Nash–Moser theorem for exact sequences of R. Hamilton to the context of deformations of Lie algebras and we discuss some aspects of the scope of this theorem in connection with the polynomial ideal associated to the variety of nilpotent Lie algebras. This allows us to introduce the space Hk-nil 2(g,g), and certain subspaces of it, that provide fine information about the deformations of g in the variety of k-step nilpotent Lie algebras. Then we focus on degenerations and rigidity in the variety of k-step nilpotent Lie algebras of dimension n with n≤7 and, in particular, we obtain rigid Lie algebras and rigid curves in the variety of 3-step nilpotent Lie algebras of dimension 7. We also recover some known results and point out a possible error in a published article related to this subject.Fil: Brega, Alfredo Oscar. 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: Cagliero, Leandro Roberto. 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: Chaves Ochoa, Augusto Enrique. 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; ArgentinaElsevier Science2017-09info: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/11336/59986Brega, Alfredo Oscar; Cagliero, Leandro Roberto; Chaves Ochoa, Augusto Enrique; The Nash–Moser theorem of Hamilton and rigidity of finite dimensional nilpotent Lie algebras; Elsevier Science; Journal Of Pure And Applied Algebra; 221; 9; 9-2017; 2250-22650022-4049CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2016.12.007info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022404916302079info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:47:43Zoai:ri.conicet.gov.ar:11336/59986instacron: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 09:47:43.757CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The Nash–Moser theorem of Hamilton and rigidity of finite dimensional nilpotent Lie algebras
title The Nash–Moser theorem of Hamilton and rigidity of finite dimensional nilpotent Lie algebras
spellingShingle The Nash–Moser theorem of Hamilton and rigidity of finite dimensional nilpotent Lie algebras
Brega, Alfredo Oscar
deformations and rigidity Lie algebras
Cohomology of Lie algebras
title_short The Nash–Moser theorem of Hamilton and rigidity of finite dimensional nilpotent Lie algebras
title_full The Nash–Moser theorem of Hamilton and rigidity of finite dimensional nilpotent Lie algebras
title_fullStr The Nash–Moser theorem of Hamilton and rigidity of finite dimensional nilpotent Lie algebras
title_full_unstemmed The Nash–Moser theorem of Hamilton and rigidity of finite dimensional nilpotent Lie algebras
title_sort The Nash–Moser theorem of Hamilton and rigidity of finite dimensional nilpotent Lie algebras
dc.creator.none.fl_str_mv Brega, Alfredo Oscar
Cagliero, Leandro Roberto
Chaves Ochoa, Augusto Enrique
author Brega, Alfredo Oscar
author_facet Brega, Alfredo Oscar
Cagliero, Leandro Roberto
Chaves Ochoa, Augusto Enrique
author_role author
author2 Cagliero, Leandro Roberto
Chaves Ochoa, Augusto Enrique
author2_role author
author
dc.subject.none.fl_str_mv deformations and rigidity Lie algebras
Cohomology of Lie algebras
topic deformations and rigidity Lie algebras
Cohomology of Lie 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 apply the Nash–Moser theorem for exact sequences of R. Hamilton to the context of deformations of Lie algebras and we discuss some aspects of the scope of this theorem in connection with the polynomial ideal associated to the variety of nilpotent Lie algebras. This allows us to introduce the space Hk-nil 2(g,g), and certain subspaces of it, that provide fine information about the deformations of g in the variety of k-step nilpotent Lie algebras. Then we focus on degenerations and rigidity in the variety of k-step nilpotent Lie algebras of dimension n with n≤7 and, in particular, we obtain rigid Lie algebras and rigid curves in the variety of 3-step nilpotent Lie algebras of dimension 7. We also recover some known results and point out a possible error in a published article related to this subject.
Fil: Brega, Alfredo Oscar. 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: Cagliero, Leandro Roberto. 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: Chaves Ochoa, Augusto Enrique. 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 We apply the Nash–Moser theorem for exact sequences of R. Hamilton to the context of deformations of Lie algebras and we discuss some aspects of the scope of this theorem in connection with the polynomial ideal associated to the variety of nilpotent Lie algebras. This allows us to introduce the space Hk-nil 2(g,g), and certain subspaces of it, that provide fine information about the deformations of g in the variety of k-step nilpotent Lie algebras. Then we focus on degenerations and rigidity in the variety of k-step nilpotent Lie algebras of dimension n with n≤7 and, in particular, we obtain rigid Lie algebras and rigid curves in the variety of 3-step nilpotent Lie algebras of dimension 7. We also recover some known results and point out a possible error in a published article related to this subject.
publishDate 2017
dc.date.none.fl_str_mv 2017-09
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/11336/59986
Brega, Alfredo Oscar; Cagliero, Leandro Roberto; Chaves Ochoa, Augusto Enrique; The Nash–Moser theorem of Hamilton and rigidity of finite dimensional nilpotent Lie algebras; Elsevier Science; Journal Of Pure And Applied Algebra; 221; 9; 9-2017; 2250-2265
0022-4049
CONICET Digital
CONICET
url http://hdl.handle.net/11336/59986
identifier_str_mv Brega, Alfredo Oscar; Cagliero, Leandro Roberto; Chaves Ochoa, Augusto Enrique; The Nash–Moser theorem of Hamilton and rigidity of finite dimensional nilpotent Lie algebras; Elsevier Science; Journal Of Pure And Applied Algebra; 221; 9; 9-2017; 2250-2265
0022-4049
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2016.12.007
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022404916302079
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 Science
publisher.none.fl_str_mv Elsevier Science
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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