Abelian balanced Hermitian structures on unimodular Lie algebras

Autores
Andrada, Adrián Marcelo; Raquel Villacampa
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let g be a 2n-dimensional unimodular Lie algebra equipped with a Hermitian structure (J; F) such that the complex structure J is abelian and the fundamental form F is balanced. We prove that the holonomy group of the associated Bismut connection reduces to a subgroup of SU(n – k), being 2k the dimension of the center of g. We determine conditions that allow a unimodular Lie algebra to admit this particular type of structures. Moreover, we give methods to construct them in arbitrary dimensions and classify them if the Lie algebra is 8-dimensional and nilpotent.
Fil: Andrada, Adrián Marcelo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; 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: Raquel Villacampa. Centro Universitario de la Defensa; España
Materia
BISMUT CONNECTION
BALANCED HERMITIAN METRIC
ABELIAN COMPLEX STRUCTURE
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:11336/59788
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/59788
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Abelian balanced Hermitian structures on unimodular Lie algebrasAndrada, Adrián MarceloRaquel VillacampaBISMUT CONNECTIONBALANCED HERMITIAN METRICABELIAN COMPLEX STRUCTUREhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let g be a 2n-dimensional unimodular Lie algebra equipped with a Hermitian structure (J; F) such that the complex structure J is abelian and the fundamental form F is balanced. We prove that the holonomy group of the associated Bismut connection reduces to a subgroup of SU(n – k), being 2k the dimension of the center of g. We determine conditions that allow a unimodular Lie algebra to admit this particular type of structures. Moreover, we give methods to construct them in arbitrary dimensions and classify them if the Lie algebra is 8-dimensional and nilpotent.Fil: Andrada, Adrián Marcelo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; 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: Raquel Villacampa. Centro Universitario de la Defensa; EspañaSpringer2016-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/59788Andrada, Adrián Marcelo; Raquel Villacampa; Abelian balanced Hermitian structures on unimodular Lie algebras; Springer; Transformation Groups; 21; 4; 12-2016; 903-9271083-4362CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00031-015-9352-7info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00031-015-9352-7info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:20:17Zoai:ri.conicet.gov.ar:11336/59788instacron: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:34982025-10-22 11:20:17.409CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Abelian balanced Hermitian structures on unimodular Lie algebras
title Abelian balanced Hermitian structures on unimodular Lie algebras
spellingShingle Abelian balanced Hermitian structures on unimodular Lie algebras
Andrada, Adrián Marcelo
BISMUT CONNECTION
BALANCED HERMITIAN METRIC
ABELIAN COMPLEX STRUCTURE
title_short Abelian balanced Hermitian structures on unimodular Lie algebras
title_full Abelian balanced Hermitian structures on unimodular Lie algebras
title_fullStr Abelian balanced Hermitian structures on unimodular Lie algebras
title_full_unstemmed Abelian balanced Hermitian structures on unimodular Lie algebras
title_sort Abelian balanced Hermitian structures on unimodular Lie algebras
dc.creator.none.fl_str_mv Andrada, Adrián Marcelo
Raquel Villacampa
author Andrada, Adrián Marcelo
author_facet Andrada, Adrián Marcelo
Raquel Villacampa
author_role author
author2 Raquel Villacampa
author2_role author
dc.subject.none.fl_str_mv BISMUT CONNECTION
BALANCED HERMITIAN METRIC
ABELIAN COMPLEX STRUCTURE
topic BISMUT CONNECTION
BALANCED HERMITIAN METRIC
ABELIAN COMPLEX STRUCTURE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let g be a 2n-dimensional unimodular Lie algebra equipped with a Hermitian structure (J; F) such that the complex structure J is abelian and the fundamental form F is balanced. We prove that the holonomy group of the associated Bismut connection reduces to a subgroup of SU(n – k), being 2k the dimension of the center of g. We determine conditions that allow a unimodular Lie algebra to admit this particular type of structures. Moreover, we give methods to construct them in arbitrary dimensions and classify them if the Lie algebra is 8-dimensional and nilpotent.
Fil: Andrada, Adrián Marcelo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; 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: Raquel Villacampa. Centro Universitario de la Defensa; España
description Let g be a 2n-dimensional unimodular Lie algebra equipped with a Hermitian structure (J; F) such that the complex structure J is abelian and the fundamental form F is balanced. We prove that the holonomy group of the associated Bismut connection reduces to a subgroup of SU(n – k), being 2k the dimension of the center of g. We determine conditions that allow a unimodular Lie algebra to admit this particular type of structures. Moreover, we give methods to construct them in arbitrary dimensions and classify them if the Lie algebra is 8-dimensional and nilpotent.
publishDate 2016
dc.date.none.fl_str_mv 2016-12
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/11336/59788
Andrada, Adrián Marcelo; Raquel Villacampa; Abelian balanced Hermitian structures on unimodular Lie algebras; Springer; Transformation Groups; 21; 4; 12-2016; 903-927
1083-4362
CONICET Digital
CONICET
url http://hdl.handle.net/11336/59788
identifier_str_mv Andrada, Adrián Marcelo; Raquel Villacampa; Abelian balanced Hermitian structures on unimodular Lie algebras; Springer; Transformation Groups; 21; 4; 12-2016; 903-927
1083-4362
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00031-015-9352-7
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00031-015-9352-7
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
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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_ 1846781691615510528
score 12.982451

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