Magnetic fields on non-singular 2-step nilpotent Lie groups

Autores
Ovando, Gabriela Paola; Subils, Mauro
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This work has a twofold purpose - the existence study of closed 2-forms, known as magnetic fields, on 2-step nilpotent Lie groups and generating examples for the non-singular family. At the Lie algebra level, while the existence of closed 2-forms for which the center is either nondegenerate or in the kernel of the 2-form, is always guaranteed, the existence of closed 2-forms for which the center is isotropic but not in the kernel of the 2-form, is a special situation. These 2-forms are called of type II. We obtain a strong obstruction for the existence on non-singular Lie algebras. Moreover, we prove that the only H-type Lie groups admitting left-invariant closed 2-forms of type II are the real, complex and quaternionic Heisenberg Lie groups of dimension three, six and seven, respectively. We also prove the non-existence of uniform magnetic fields under certain hypotheses. Finally we give a construction of non-singular Lie algebras, proving that in some families of these examples there are no closed 2-form of type II.
Fil: Ovando, Gabriela Paola. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Subils, Mauro. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Materia
2-STEP NILMANIFOLDS
CLOSED 2-FORMS
H-TYPE LIE GROUPS
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:11336/230975
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Magnetic fields on non-singular 2-step nilpotent Lie groupsOvando, Gabriela PaolaSubils, Mauro2-STEP NILMANIFOLDSCLOSED 2-FORMSH-TYPE LIE GROUPShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This work has a twofold purpose - the existence study of closed 2-forms, known as magnetic fields, on 2-step nilpotent Lie groups and generating examples for the non-singular family. At the Lie algebra level, while the existence of closed 2-forms for which the center is either nondegenerate or in the kernel of the 2-form, is always guaranteed, the existence of closed 2-forms for which the center is isotropic but not in the kernel of the 2-form, is a special situation. These 2-forms are called of type II. We obtain a strong obstruction for the existence on non-singular Lie algebras. Moreover, we prove that the only H-type Lie groups admitting left-invariant closed 2-forms of type II are the real, complex and quaternionic Heisenberg Lie groups of dimension three, six and seven, respectively. We also prove the non-existence of uniform magnetic fields under certain hypotheses. Finally we give a construction of non-singular Lie algebras, proving that in some families of these examples there are no closed 2-form of type II.Fil: Ovando, Gabriela Paola. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Subils, Mauro. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaElsevier Science2024-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/230975Ovando, Gabriela Paola; Subils, Mauro; Magnetic fields on non-singular 2-step nilpotent Lie groups; Elsevier Science; Journal Of Pure And Applied Algebra; 228; 6; 6-2024; 11-260022-4049CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2024.107618info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S002240492400015Xinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/pdf/2210.12180.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:04:31Zoai:ri.conicet.gov.ar:11336/230975instacron: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 11:04:31.967CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Magnetic fields on non-singular 2-step nilpotent Lie groups
title Magnetic fields on non-singular 2-step nilpotent Lie groups
spellingShingle Magnetic fields on non-singular 2-step nilpotent Lie groups
Ovando, Gabriela Paola
2-STEP NILMANIFOLDS
CLOSED 2-FORMS
H-TYPE LIE GROUPS
title_short Magnetic fields on non-singular 2-step nilpotent Lie groups
title_full Magnetic fields on non-singular 2-step nilpotent Lie groups
title_fullStr Magnetic fields on non-singular 2-step nilpotent Lie groups
title_full_unstemmed Magnetic fields on non-singular 2-step nilpotent Lie groups
title_sort Magnetic fields on non-singular 2-step nilpotent Lie groups
dc.creator.none.fl_str_mv Ovando, Gabriela Paola
Subils, Mauro
author Ovando, Gabriela Paola
author_facet Ovando, Gabriela Paola
Subils, Mauro
author_role author
author2 Subils, Mauro
author2_role author
dc.subject.none.fl_str_mv 2-STEP NILMANIFOLDS
CLOSED 2-FORMS
H-TYPE LIE GROUPS
topic 2-STEP NILMANIFOLDS
CLOSED 2-FORMS
H-TYPE LIE GROUPS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This work has a twofold purpose - the existence study of closed 2-forms, known as magnetic fields, on 2-step nilpotent Lie groups and generating examples for the non-singular family. At the Lie algebra level, while the existence of closed 2-forms for which the center is either nondegenerate or in the kernel of the 2-form, is always guaranteed, the existence of closed 2-forms for which the center is isotropic but not in the kernel of the 2-form, is a special situation. These 2-forms are called of type II. We obtain a strong obstruction for the existence on non-singular Lie algebras. Moreover, we prove that the only H-type Lie groups admitting left-invariant closed 2-forms of type II are the real, complex and quaternionic Heisenberg Lie groups of dimension three, six and seven, respectively. We also prove the non-existence of uniform magnetic fields under certain hypotheses. Finally we give a construction of non-singular Lie algebras, proving that in some families of these examples there are no closed 2-form of type II.
Fil: Ovando, Gabriela Paola. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Subils, Mauro. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
description This work has a twofold purpose - the existence study of closed 2-forms, known as magnetic fields, on 2-step nilpotent Lie groups and generating examples for the non-singular family. At the Lie algebra level, while the existence of closed 2-forms for which the center is either nondegenerate or in the kernel of the 2-form, is always guaranteed, the existence of closed 2-forms for which the center is isotropic but not in the kernel of the 2-form, is a special situation. These 2-forms are called of type II. We obtain a strong obstruction for the existence on non-singular Lie algebras. Moreover, we prove that the only H-type Lie groups admitting left-invariant closed 2-forms of type II are the real, complex and quaternionic Heisenberg Lie groups of dimension three, six and seven, respectively. We also prove the non-existence of uniform magnetic fields under certain hypotheses. Finally we give a construction of non-singular Lie algebras, proving that in some families of these examples there are no closed 2-form of type II.
publishDate 2024
dc.date.none.fl_str_mv 2024-06
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/11336/230975
Ovando, Gabriela Paola; Subils, Mauro; Magnetic fields on non-singular 2-step nilpotent Lie groups; Elsevier Science; Journal Of Pure And Applied Algebra; 228; 6; 6-2024; 11-26
0022-4049
CONICET Digital
CONICET
url http://hdl.handle.net/11336/230975
identifier_str_mv Ovando, Gabriela Paola; Subils, Mauro; Magnetic fields on non-singular 2-step nilpotent Lie groups; Elsevier Science; Journal Of Pure And Applied Algebra; 228; 6; 6-2024; 11-26
0022-4049
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2024.107618
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S002240492400015X
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/pdf/2210.12180.pdf
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
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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 12.982451

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