Isomorphism and Isotopism Classes of Filiform Lie Algebras of Dimension up to Seven Over Finite Fields

Since the introduction of the concept of isotopism of algebras by Albert in 1942, a prolific literature on the subject has been developed for distinct types of algebras. Nevertheless, there barely exists any result on the problem of distributing Lie algebras into isotopism classes. The current paper...

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Autores: Falcón Ganfornina, Óscar Jesús, Falcón Ganfornina, Raúl Manuel, Núñez Valdés, Juan
Formato: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2016
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/47961
Acesso em linha:http://hdl.handle.net/11441/47961
https://doi.org/10.1007/s00025-016-0616-x
Access Level:acceso abierto
Palavra-chave:Filiform Lie algebra
Isotopism
Isomorphism
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spelling Isomorphism and Isotopism Classes of Filiform Lie Algebras of Dimension up to Seven Over Finite FieldsFalcón Ganfornina, Óscar JesúsFalcón Ganfornina, Raúl ManuelNúñez Valdés, JuanFiliform Lie algebraIsotopismIsomorphismSince the introduction of the concept of isotopism of algebras by Albert in 1942, a prolific literature on the subject has been developed for distinct types of algebras. Nevertheless, there barely exists any result on the problem of distributing Lie algebras into isotopism classes. The current paper is a first step to deal with such a problem. Specifically, we define a new series of isotopism invariants and we determine explicitly the distribution into isotopism classes of n-dimensional filiform Lie algebras, for n ≤ 7. We also deal with the distribution of such algebras into isomorphism classes, for which we confirm some known results and we prove that there exist p + 8 isomorphism classes of seven-dimensional filiform Lie algebras over the finite field Fp if p ≠ 2.SpringerMatemática Aplicada IGeometría y TopologíaFQM016: Códigos, Diseños, Criptografía y OptimizaciónFQM326: Geometria Diferencial y Teoria de Lie2016info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/47961https://doi.org/10.1007/s00025-016-0616-xreponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésResults in Mathematics, 1-16.http://dx.doi.org/10.1007/s00025-016-0616-xinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/479612026-06-17T12:51:07Z
dc.title.none.fl_str_mv Isomorphism and Isotopism Classes of Filiform Lie Algebras of Dimension up to Seven Over Finite Fields
title Isomorphism and Isotopism Classes of Filiform Lie Algebras of Dimension up to Seven Over Finite Fields
spellingShingle Isomorphism and Isotopism Classes of Filiform Lie Algebras of Dimension up to Seven Over Finite Fields
Falcón Ganfornina, Óscar Jesús
Filiform Lie algebra
Isotopism
Isomorphism
title_short Isomorphism and Isotopism Classes of Filiform Lie Algebras of Dimension up to Seven Over Finite Fields
title_full Isomorphism and Isotopism Classes of Filiform Lie Algebras of Dimension up to Seven Over Finite Fields
title_fullStr Isomorphism and Isotopism Classes of Filiform Lie Algebras of Dimension up to Seven Over Finite Fields
title_full_unstemmed Isomorphism and Isotopism Classes of Filiform Lie Algebras of Dimension up to Seven Over Finite Fields
title_sort Isomorphism and Isotopism Classes of Filiform Lie Algebras of Dimension up to Seven Over Finite Fields
dc.creator.none.fl_str_mv Falcón Ganfornina, Óscar Jesús
Falcón Ganfornina, Raúl Manuel
Núñez Valdés, Juan
author Falcón Ganfornina, Óscar Jesús
author_facet Falcón Ganfornina, Óscar Jesús
Falcón Ganfornina, Raúl Manuel
Núñez Valdés, Juan
author_role author
author2 Falcón Ganfornina, Raúl Manuel
Núñez Valdés, Juan
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
Geometría y Topología
FQM016: Códigos, Diseños, Criptografía y Optimización
FQM326: Geometria Diferencial y Teoria de Lie
dc.subject.none.fl_str_mv Filiform Lie algebra
Isotopism
Isomorphism
topic Filiform Lie algebra
Isotopism
Isomorphism
description Since the introduction of the concept of isotopism of algebras by Albert in 1942, a prolific literature on the subject has been developed for distinct types of algebras. Nevertheless, there barely exists any result on the problem of distributing Lie algebras into isotopism classes. The current paper is a first step to deal with such a problem. Specifically, we define a new series of isotopism invariants and we determine explicitly the distribution into isotopism classes of n-dimensional filiform Lie algebras, for n ≤ 7. We also deal with the distribution of such algebras into isomorphism classes, for which we confirm some known results and we prove that there exist p + 8 isomorphism classes of seven-dimensional filiform Lie algebras over the finite field Fp if p ≠ 2.
publishDate 2016
dc.date.none.fl_str_mv 2016
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/47961
https://doi.org/10.1007/s00025-016-0616-x
url http://hdl.handle.net/11441/47961
https://doi.org/10.1007/s00025-016-0616-x
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Results in Mathematics, 1-16.
http://dx.doi.org/10.1007/s00025-016-0616-x
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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