Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radical

Let g = s n r be an indecomposable Lie algebra with nontrivial semisimple Levi subalgebra s and nontrivial solvable radical r. In this note it is proved that r cannot be isomorphic to a filiform nilpotent Lie algebra. The proof uses the fact that any Lie algebra g = snr with filiform radical would d...

ver descrição completa

Detalhes bibliográficos
Autores: Ancochea Bermúdez, José María, Campoamor Stursberg, Otto-Rudwig, García Vergnolle, Lucía
Formato: artículo
Fecha de publicación:2006
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/50562
Acesso em linha:https://hdl.handle.net/20.500.14352/50562
Access Level:acceso abierto
Palavra-chave:512.554.3
Lie algebra
Levi decomposition
radical
Álgebra
1201 Álgebra
id ES_704112bc6d2df2402a2fcc6b9978a596
oai_identifier_str oai:docta.ucm.es:20.500.14352/50562
network_acronym_str ES
network_name_str España
repository_id_str
spelling Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radicalAncochea Bermúdez, José MaríaCampoamor Stursberg, Otto-RudwigGarcía Vergnolle, Lucía512.554.3Lie algebraLevi decompositionradicalÁlgebra1201 ÁlgebraLet g = s n r be an indecomposable Lie algebra with nontrivial semisimple Levi subalgebra s and nontrivial solvable radical r. In this note it is proved that r cannot be isomorphic to a filiform nilpotent Lie algebra. The proof uses the fact that any Lie algebra g = snr with filiform radical would degenerate (even contract) to the Lie algebra snfn, where fn is the standard graded filiform Lie algebra of dimension n = dim r. This leads to a contradiction, since no such indecomposable algebra snr with r = fn existsHikariUniversidad Complutense de Madrid20062006-01-0120062006-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/50562reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/505622026-06-02T12:44:21Z
dc.title.none.fl_str_mv Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radical
title Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radical
spellingShingle Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radical
Ancochea Bermúdez, José María
512.554.3
Lie algebra
Levi decomposition
radical
Álgebra
1201 Álgebra
title_short Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radical
title_full Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radical
title_fullStr Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radical
title_full_unstemmed Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radical
title_sort Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radical
dc.creator.none.fl_str_mv Ancochea Bermúdez, José María
Campoamor Stursberg, Otto-Rudwig
García Vergnolle, Lucía
author Ancochea Bermúdez, José María
author_facet Ancochea Bermúdez, José María
Campoamor Stursberg, Otto-Rudwig
García Vergnolle, Lucía
author_role author
author2 Campoamor Stursberg, Otto-Rudwig
García Vergnolle, Lucía
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 512.554.3
Lie algebra
Levi decomposition
radical
Álgebra
1201 Álgebra
topic 512.554.3
Lie algebra
Levi decomposition
radical
Álgebra
1201 Álgebra
description Let g = s n r be an indecomposable Lie algebra with nontrivial semisimple Levi subalgebra s and nontrivial solvable radical r. In this note it is proved that r cannot be isomorphic to a filiform nilpotent Lie algebra. The proof uses the fact that any Lie algebra g = snr with filiform radical would degenerate (even contract) to the Lie algebra snfn, where fn is the standard graded filiform Lie algebra of dimension n = dim r. This leads to a contradiction, since no such indecomposable algebra snr with r = fn exists
publishDate 2006
dc.date.none.fl_str_mv 2006
2006-01-01
2006
2006-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/50562
url https://hdl.handle.net/20.500.14352/50562
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Hikari
publisher.none.fl_str_mv Hikari
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869410567470448640
score 15,300719

Registos relacionados