Locally conformal symplectic structures on Lie algebras of type i and their solvmanifolds

Autores
Origlia, Marcos Miguel
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study Lie algebras of type I, that is, a Lie algebra g where all the eigenvalues of the operator ad X are imaginary for all X g. We prove that the Morse-Novikov cohomology of a Lie algebra of type I is trivial for any closed 1-form. We focus on locally conformal symplectic structures (LCS) on Lie algebras of type I. In particular, we show that for a Lie algebra of type I any LCS structure is of the first kind. We also exhibit lattices for some 6-dimensional Lie groups of type I admitting left invariant LCS structures in order to produce compact solvmanifolds equipped with an invariant LCS structure.
Fil: Origlia, Marcos Miguel. Katholikie Universiteit Leuven; Bélgica. 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
LATTICE
LIE ALGEBRAS OF TYPE I
LOCALLY CONFORMAL KÄHLER METRIC
LOCALLY CONFORMAL SYMPLECTIC STRUCTURE
SOLVMANIFOLD
VAISMAN METRIC
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:11336/125022
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/125022
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Locally conformal symplectic structures on Lie algebras of type i and their solvmanifoldsOriglia, Marcos MiguelLATTICELIE ALGEBRAS OF TYPE ILOCALLY CONFORMAL KÄHLER METRICLOCALLY CONFORMAL SYMPLECTIC STRUCTURESOLVMANIFOLDVAISMAN METRIChttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study Lie algebras of type I, that is, a Lie algebra g where all the eigenvalues of the operator ad X are imaginary for all X g. We prove that the Morse-Novikov cohomology of a Lie algebra of type I is trivial for any closed 1-form. We focus on locally conformal symplectic structures (LCS) on Lie algebras of type I. In particular, we show that for a Lie algebra of type I any LCS structure is of the first kind. We also exhibit lattices for some 6-dimensional Lie groups of type I admitting left invariant LCS structures in order to produce compact solvmanifolds equipped with an invariant LCS structure.Fil: Origlia, Marcos Miguel. Katholikie Universiteit Leuven; Bélgica. 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; ArgentinaDe Gruyter2019-05-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/125022Origlia, Marcos Miguel; Locally conformal symplectic structures on Lie algebras of type i and their solvmanifolds; De Gruyter; Forum Mathematicum; 31; 3; 1-5-2019; 563-5780933-77411435-5337CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1515/forum-2018-0200info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/journals/form/31/3/article-p563.xmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:23:48Zoai:ri.conicet.gov.ar:11336/125022instacron: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:34982025-09-10 13:23:48.486CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Locally conformal symplectic structures on Lie algebras of type i and their solvmanifolds
title Locally conformal symplectic structures on Lie algebras of type i and their solvmanifolds
spellingShingle Locally conformal symplectic structures on Lie algebras of type i and their solvmanifolds
Origlia, Marcos Miguel
LATTICE
LIE ALGEBRAS OF TYPE I
LOCALLY CONFORMAL KÄHLER METRIC
LOCALLY CONFORMAL SYMPLECTIC STRUCTURE
SOLVMANIFOLD
VAISMAN METRIC
title_short Locally conformal symplectic structures on Lie algebras of type i and their solvmanifolds
title_full Locally conformal symplectic structures on Lie algebras of type i and their solvmanifolds
title_fullStr Locally conformal symplectic structures on Lie algebras of type i and their solvmanifolds
title_full_unstemmed Locally conformal symplectic structures on Lie algebras of type i and their solvmanifolds
title_sort Locally conformal symplectic structures on Lie algebras of type i and their solvmanifolds
dc.creator.none.fl_str_mv Origlia, Marcos Miguel
author Origlia, Marcos Miguel
author_facet Origlia, Marcos Miguel
author_role author
dc.subject.none.fl_str_mv LATTICE
LIE ALGEBRAS OF TYPE I
LOCALLY CONFORMAL KÄHLER METRIC
LOCALLY CONFORMAL SYMPLECTIC STRUCTURE
SOLVMANIFOLD
VAISMAN METRIC
topic LATTICE
LIE ALGEBRAS OF TYPE I
LOCALLY CONFORMAL KÄHLER METRIC
LOCALLY CONFORMAL SYMPLECTIC STRUCTURE
SOLVMANIFOLD
VAISMAN METRIC
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 study Lie algebras of type I, that is, a Lie algebra g where all the eigenvalues of the operator ad X are imaginary for all X g. We prove that the Morse-Novikov cohomology of a Lie algebra of type I is trivial for any closed 1-form. We focus on locally conformal symplectic structures (LCS) on Lie algebras of type I. In particular, we show that for a Lie algebra of type I any LCS structure is of the first kind. We also exhibit lattices for some 6-dimensional Lie groups of type I admitting left invariant LCS structures in order to produce compact solvmanifolds equipped with an invariant LCS structure.
Fil: Origlia, Marcos Miguel. Katholikie Universiteit Leuven; Bélgica. 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 study Lie algebras of type I, that is, a Lie algebra g where all the eigenvalues of the operator ad X are imaginary for all X g. We prove that the Morse-Novikov cohomology of a Lie algebra of type I is trivial for any closed 1-form. We focus on locally conformal symplectic structures (LCS) on Lie algebras of type I. In particular, we show that for a Lie algebra of type I any LCS structure is of the first kind. We also exhibit lattices for some 6-dimensional Lie groups of type I admitting left invariant LCS structures in order to produce compact solvmanifolds equipped with an invariant LCS structure.
publishDate 2019
dc.date.none.fl_str_mv 2019-05-01
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/11336/125022
Origlia, Marcos Miguel; Locally conformal symplectic structures on Lie algebras of type i and their solvmanifolds; De Gruyter; Forum Mathematicum; 31; 3; 1-5-2019; 563-578
0933-7741
1435-5337
CONICET Digital
CONICET
url http://hdl.handle.net/11336/125022
identifier_str_mv Origlia, Marcos Miguel; Locally conformal symplectic structures on Lie algebras of type i and their solvmanifolds; De Gruyter; Forum Mathematicum; 31; 3; 1-5-2019; 563-578
0933-7741
1435-5337
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1515/forum-2018-0200
info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/journals/form/31/3/article-p563.xml
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
dc.publisher.none.fl_str_mv De Gruyter
publisher.none.fl_str_mv De Gruyter
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 12.48226

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