There are no rigid filiform Lie algebras of low dimension

Autores
Vera, Sonia Vanesa; Tirao, Paulo Andres
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove that there are no rigid complex filiform Lie algebras in the variety of (filiform) Lie algebras of dimension less than or equal to 11. More precisely we show that in any Euclidean neighborhood of a filiform Lie bracket (of low dimension), there is a non-isomorphic filiform Lie bracket. This follows by constructing non-trivial linear deformations in a Zariski open dense set of the variety of filiform Lie algebras of dimension 9, 10 and 11 (in lower dimensions this is well known.)
Fil: Vera, Sonia Vanesa. Universidad Nacional de Córdoba; Argentina. 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: Tirao, Paulo Andres. Universidad Nacional de Córdoba; Argentina. 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
FILIFORMS LIE ALGEBRAS
DEFORMATIONS
VERGNE'S CONJETURE
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:11336/125072
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling There are no rigid filiform Lie algebras of low dimensionVera, Sonia VanesaTirao, Paulo AndresFILIFORMS LIE ALGEBRASDEFORMATIONSVERGNE'S CONJETUREhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove that there are no rigid complex filiform Lie algebras in the variety of (filiform) Lie algebras of dimension less than or equal to 11. More precisely we show that in any Euclidean neighborhood of a filiform Lie bracket (of low dimension), there is a non-isomorphic filiform Lie bracket. This follows by constructing non-trivial linear deformations in a Zariski open dense set of the variety of filiform Lie algebras of dimension 9, 10 and 11 (in lower dimensions this is well known.)Fil: Vera, Sonia Vanesa. Universidad Nacional de Córdoba; Argentina. 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: Tirao, Paulo Andres. Universidad Nacional de Córdoba; Argentina. 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; ArgentinaHeldermann Verlag2019-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/125072Vera, Sonia Vanesa; Tirao, Paulo Andres; There are no rigid filiform Lie algebras of low dimension; Heldermann Verlag; Journal Of Lie Theory; 29; 2; 1-2019; 391-4120949-5932CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.heldermann.de/JLT/JLT29/JLT292/jlt29019.htminfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1709.04793info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:09:53Zoai:ri.conicet.gov.ar:11336/125072instacron: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 10:09:53.517CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv There are no rigid filiform Lie algebras of low dimension
title There are no rigid filiform Lie algebras of low dimension
spellingShingle There are no rigid filiform Lie algebras of low dimension
Vera, Sonia Vanesa
FILIFORMS LIE ALGEBRAS
DEFORMATIONS
VERGNE'S CONJETURE
title_short There are no rigid filiform Lie algebras of low dimension
title_full There are no rigid filiform Lie algebras of low dimension
title_fullStr There are no rigid filiform Lie algebras of low dimension
title_full_unstemmed There are no rigid filiform Lie algebras of low dimension
title_sort There are no rigid filiform Lie algebras of low dimension
dc.creator.none.fl_str_mv Vera, Sonia Vanesa
Tirao, Paulo Andres
author Vera, Sonia Vanesa
author_facet Vera, Sonia Vanesa
Tirao, Paulo Andres
author_role author
author2 Tirao, Paulo Andres
author2_role author
dc.subject.none.fl_str_mv FILIFORMS LIE ALGEBRAS
DEFORMATIONS
VERGNE'S CONJETURE
topic FILIFORMS LIE ALGEBRAS
DEFORMATIONS
VERGNE'S CONJETURE
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 prove that there are no rigid complex filiform Lie algebras in the variety of (filiform) Lie algebras of dimension less than or equal to 11. More precisely we show that in any Euclidean neighborhood of a filiform Lie bracket (of low dimension), there is a non-isomorphic filiform Lie bracket. This follows by constructing non-trivial linear deformations in a Zariski open dense set of the variety of filiform Lie algebras of dimension 9, 10 and 11 (in lower dimensions this is well known.)
Fil: Vera, Sonia Vanesa. Universidad Nacional de Córdoba; Argentina. 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: Tirao, Paulo Andres. Universidad Nacional de Córdoba; Argentina. 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 prove that there are no rigid complex filiform Lie algebras in the variety of (filiform) Lie algebras of dimension less than or equal to 11. More precisely we show that in any Euclidean neighborhood of a filiform Lie bracket (of low dimension), there is a non-isomorphic filiform Lie bracket. This follows by constructing non-trivial linear deformations in a Zariski open dense set of the variety of filiform Lie algebras of dimension 9, 10 and 11 (in lower dimensions this is well known.)
publishDate 2019
dc.date.none.fl_str_mv 2019-01
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/11336/125072
Vera, Sonia Vanesa; Tirao, Paulo Andres; There are no rigid filiform Lie algebras of low dimension; Heldermann Verlag; Journal Of Lie Theory; 29; 2; 1-2019; 391-412
0949-5932
CONICET Digital
CONICET
url http://hdl.handle.net/11336/125072
identifier_str_mv Vera, Sonia Vanesa; Tirao, Paulo Andres; There are no rigid filiform Lie algebras of low dimension; Heldermann Verlag; Journal Of Lie Theory; 29; 2; 1-2019; 391-412
0949-5932
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.heldermann.de/JLT/JLT29/JLT292/jlt29019.htm
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1709.04793
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
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Heldermann Verlag
publisher.none.fl_str_mv Heldermann Verlag
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
_version_ 1842270097939365888
score 13.13397

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