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

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 spac...

Descripción completa

Detalles Bibliográficos
Autores: Brega, Alfredo Oscar, Cagliero, Leandro Roberto, Chaves Ochoa, Augusto Enrique
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/59986
Acceso en línea:http://hdl.handle.net/11336/59986
Access Level:acceso abierto
Palabra clave:deformations and rigidity Lie algebras
Cohomology of Lie algebras
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
id AR_f2bfceafa6c3d39e0c80e76c50f72ef7
oai_identifier_str oai:ri.conicet.gov.ar:11336/59986
network_acronym_str AR
network_name_str Argentina
repository_id_str
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 Técnicas2024-05-08T13:38:24Zoai: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:34982024-05-08 13:38:25.042CONICET 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
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic deformations and rigidity Lie algebras
Cohomology of Lie algebras
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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
_version_ 1799194874124173312
score 15,812429

Similares en LA Referencia