Some cohomologically rigid solvable Leibniz algebras

In this paper we describe solvable Leibniz algebras whose quotient algebra by one-dimensional ideal is a Lie algebra with rank equal to the length of the characteristic sequence of its nilpotent radical. We prove that such Leibniz algebra is unique and centerless. Also it is proved that the first an...

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Detalles Bibliográficos
Autores: Camacho Santana, Luisa María, Kaygorodov, Ivan, Omirov, Bakhrom Abdazovich, Solijanova, Gulkhayo
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2020
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/115106
Acceso en línea:https://hdl.handle.net/11441/115106
https://doi.org/10.1016/j.jalgebra.2020.05.033
Access Level:acceso abierto
Palabra clave:Lie algebras
Leibniz algebra
Nilpotent radical
Characteristic sequence
Solvable algebra
Derivations
2-Cocycle
Rigid algebra
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spelling Some cohomologically rigid solvable Leibniz algebrasCamacho Santana, Luisa MaríaKaygorodov, IvanOmirov, Bakhrom AbdazovichSolijanova, GulkhayoLie algebrasLeibniz algebraNilpotent radicalCharacteristic sequenceSolvable algebraDerivations2-CocycleRigid algebraIn this paper we describe solvable Leibniz algebras whose quotient algebra by one-dimensional ideal is a Lie algebra with rank equal to the length of the characteristic sequence of its nilpotent radical. We prove that such Leibniz algebra is unique and centerless. Also it is proved that the first and the second cohomology groups of the algebra with coefficients in the adjoint representation is trivial.Ministerio de Economía y Competitividad MTM2016-79661-PElsevierMatemática Aplicada IMinisterio de Economía y Competitividad (MINECO). España2020info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/115106https://doi.org/10.1016/j.jalgebra.2020.05.033reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Algebra, 560 (October 2020), 502-520.MTM2016-79661-Phttps://www.sciencedirect.com/science/article/pii/S0021869320302994info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1151062026-06-17T12:51:07Z
dc.title.none.fl_str_mv Some cohomologically rigid solvable Leibniz algebras
title Some cohomologically rigid solvable Leibniz algebras
spellingShingle Some cohomologically rigid solvable Leibniz algebras
Camacho Santana, Luisa María
Lie algebras
Leibniz algebra
Nilpotent radical
Characteristic sequence
Solvable algebra
Derivations
2-Cocycle
Rigid algebra
title_short Some cohomologically rigid solvable Leibniz algebras
title_full Some cohomologically rigid solvable Leibniz algebras
title_fullStr Some cohomologically rigid solvable Leibniz algebras
title_full_unstemmed Some cohomologically rigid solvable Leibniz algebras
title_sort Some cohomologically rigid solvable Leibniz algebras
dc.creator.none.fl_str_mv Camacho Santana, Luisa María
Kaygorodov, Ivan
Omirov, Bakhrom Abdazovich
Solijanova, Gulkhayo
author Camacho Santana, Luisa María
author_facet Camacho Santana, Luisa María
Kaygorodov, Ivan
Omirov, Bakhrom Abdazovich
Solijanova, Gulkhayo
author_role author
author2 Kaygorodov, Ivan
Omirov, Bakhrom Abdazovich
Solijanova, Gulkhayo
author2_role author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
Ministerio de Economía y Competitividad (MINECO). España
dc.subject.none.fl_str_mv Lie algebras
Leibniz algebra
Nilpotent radical
Characteristic sequence
Solvable algebra
Derivations
2-Cocycle
Rigid algebra
topic Lie algebras
Leibniz algebra
Nilpotent radical
Characteristic sequence
Solvable algebra
Derivations
2-Cocycle
Rigid algebra
description In this paper we describe solvable Leibniz algebras whose quotient algebra by one-dimensional ideal is a Lie algebra with rank equal to the length of the characteristic sequence of its nilpotent radical. We prove that such Leibniz algebra is unique and centerless. Also it is proved that the first and the second cohomology groups of the algebra with coefficients in the adjoint representation is trivial.
publishDate 2020
dc.date.none.fl_str_mv 2020
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 https://hdl.handle.net/11441/115106
https://doi.org/10.1016/j.jalgebra.2020.05.033
url https://hdl.handle.net/11441/115106
https://doi.org/10.1016/j.jalgebra.2020.05.033
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Algebra, 560 (October 2020), 502-520.
MTM2016-79661-P
https://www.sciencedirect.com/science/article/pii/S0021869320302994
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 Elsevier
publisher.none.fl_str_mv Elsevier
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 15,300719

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