Symplectic structures on nilmanifolds: an obstruction for its existence

Autores
del Barco, Viviana Jorgelina
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this work we introduce an obstruction for the existence of symplectic structures on nilpotent Lie algebras. Indeed, a necessary condition is presented in terms of the cohomology of the Lie algebra. Using this obstruction we obtain both positive and negative results on the existence of symplectic structures on a large family of nilpotent Lie algebras. Namely the family of nilradicals of minimal parabolic subalgebras associated to the real split Lie algebra of classical complex simple Lie algebras.
Fil: del Barco, Viviana Jorgelina. Universidad Nacional de Rosario. Facultad de Cs.exactas Ingeniería y Agrimensura. Escuela de Cs.exactas y Naturales. Departamento de Matemática; Argentina
Materia
Symplectic Structures
Nilpotent Lie Algebras
Lie Algebra Cohomology
Minimal Parabolic Subalgebras
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:11336/30806
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Symplectic structures on nilmanifolds: an obstruction for its existencedel Barco, Viviana JorgelinaSymplectic StructuresNilpotent Lie AlgebrasLie Algebra CohomologyMinimal Parabolic Subalgebrashttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this work we introduce an obstruction for the existence of symplectic structures on nilpotent Lie algebras. Indeed, a necessary condition is presented in terms of the cohomology of the Lie algebra. Using this obstruction we obtain both positive and negative results on the existence of symplectic structures on a large family of nilpotent Lie algebras. Namely the family of nilradicals of minimal parabolic subalgebras associated to the real split Lie algebra of classical complex simple Lie algebras.Fil: del Barco, Viviana Jorgelina. Universidad Nacional de Rosario. Facultad de Cs.exactas Ingeniería y Agrimensura. Escuela de Cs.exactas y Naturales. Departamento de Matemática; ArgentinaHeldermann Verlag2014-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/vnd.rarapplication/pdfhttp://hdl.handle.net/11336/30806Symplectic structures on nilmanifolds: an obstruction for its existence; Heldermann Verlag; Journal Of Lie Theory; 24; 3; 8-2014; 889-9080949-5932CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1210.6296info:eu-repo/semantics/altIdentifier/url/http://www.heldermann.de/JLT/JLT24/JLT243/jlt24039.htminfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:37:23Zoai:ri.conicet.gov.ar:11336/30806instacron: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:34982025-09-29 09:37:23.785CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Symplectic structures on nilmanifolds: an obstruction for its existence
title Symplectic structures on nilmanifolds: an obstruction for its existence
spellingShingle Symplectic structures on nilmanifolds: an obstruction for its existence
del Barco, Viviana Jorgelina
Symplectic Structures
Nilpotent Lie Algebras
Lie Algebra Cohomology
Minimal Parabolic Subalgebras
title_short Symplectic structures on nilmanifolds: an obstruction for its existence
title_full Symplectic structures on nilmanifolds: an obstruction for its existence
title_fullStr Symplectic structures on nilmanifolds: an obstruction for its existence
title_full_unstemmed Symplectic structures on nilmanifolds: an obstruction for its existence
title_sort Symplectic structures on nilmanifolds: an obstruction for its existence
dc.creator.none.fl_str_mv del Barco, Viviana Jorgelina
author del Barco, Viviana Jorgelina
author_facet del Barco, Viviana Jorgelina
author_role author
dc.subject.none.fl_str_mv Symplectic Structures
Nilpotent Lie Algebras
Lie Algebra Cohomology
Minimal Parabolic Subalgebras
topic Symplectic Structures
Nilpotent Lie Algebras
Lie Algebra Cohomology
Minimal Parabolic Subalgebras
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this work we introduce an obstruction for the existence of symplectic structures on nilpotent Lie algebras. Indeed, a necessary condition is presented in terms of the cohomology of the Lie algebra. Using this obstruction we obtain both positive and negative results on the existence of symplectic structures on a large family of nilpotent Lie algebras. Namely the family of nilradicals of minimal parabolic subalgebras associated to the real split Lie algebra of classical complex simple Lie algebras.
Fil: del Barco, Viviana Jorgelina. Universidad Nacional de Rosario. Facultad de Cs.exactas Ingeniería y Agrimensura. Escuela de Cs.exactas y Naturales. Departamento de Matemática; Argentina
description In this work we introduce an obstruction for the existence of symplectic structures on nilpotent Lie algebras. Indeed, a necessary condition is presented in terms of the cohomology of the Lie algebra. Using this obstruction we obtain both positive and negative results on the existence of symplectic structures on a large family of nilpotent Lie algebras. Namely the family of nilradicals of minimal parabolic subalgebras associated to the real split Lie algebra of classical complex simple Lie algebras.
publishDate 2014
dc.date.none.fl_str_mv 2014-08
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/11336/30806
Symplectic structures on nilmanifolds: an obstruction for its existence; Heldermann Verlag; Journal Of Lie Theory; 24; 3; 8-2014; 889-908
0949-5932
CONICET Digital
CONICET
url http://hdl.handle.net/11336/30806
identifier_str_mv Symplectic structures on nilmanifolds: an obstruction for its existence; Heldermann Verlag; Journal Of Lie Theory; 24; 3; 8-2014; 889-908
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/arxiv/https://arxiv.org/abs/1210.6296
info:eu-repo/semantics/altIdentifier/url/http://www.heldermann.de/JLT/JLT24/JLT243/jlt24039.htm
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/vnd.rar
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
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score 13.070432

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