Classification of 7-dimensional einstein nilradicals

Autores
Fernández Culma, Edison Alberto
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The problem of classifying Einstein solvmanifolds, or equivalently, Ricci soliton nilmanifolds, is known to be equivalent to a question on the variety N n(ℂ) of n-dimensional complex nilpotent Lie algebra laws. Namely, one has to determine which GL n(ℂ)-orbits in N n(ℂ) have a critical point of the squared norm of the moment map. In this paper, we give a classification result of such distinguished orbits for n = 7. The set N 7(ℂ)/GL 7(ℂ) is formed by 148 nilpotent Lie algebras and 6 one-parameter families of pairwise non-isomorphic nilpotent Lie algebras. We have applied to each Lie algebra one of three main techniques to decide whether it has a distinguished orbit or not.
Fil: Fernández Culma, Edison Alberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; 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
EINSTEIN MANIFOLDS
EINSTEIN NILRADICAL
NILSOLITONS
GEOMETRIC INVARIANT THEORY
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:11336/198380
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/198380
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Classification of 7-dimensional einstein nilradicalsFernández Culma, Edison AlbertoEINSTEIN MANIFOLDSEINSTEIN NILRADICALNILSOLITONSGEOMETRIC INVARIANT THEORYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The problem of classifying Einstein solvmanifolds, or equivalently, Ricci soliton nilmanifolds, is known to be equivalent to a question on the variety N n(ℂ) of n-dimensional complex nilpotent Lie algebra laws. Namely, one has to determine which GL n(ℂ)-orbits in N n(ℂ) have a critical point of the squared norm of the moment map. In this paper, we give a classification result of such distinguished orbits for n = 7. The set N 7(ℂ)/GL 7(ℂ) is formed by 148 nilpotent Lie algebras and 6 one-parameter families of pairwise non-isomorphic nilpotent Lie algebras. We have applied to each Lie algebra one of three main techniques to decide whether it has a distinguished orbit or not.Fil: Fernández Culma, Edison Alberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; 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; ArgentinaBirkhauser Boston Inc2012-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/198380Fernández Culma, Edison Alberto; Classification of 7-dimensional einstein nilradicals; Birkhauser Boston Inc; Transformation Groups; 17; 3; 8-2012; 639-6561083-43621531-586XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs00031-012-9186-5info:eu-repo/semantics/altIdentifier/doi/10.1007/s00031-012-9186-5info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:14:34Zoai:ri.conicet.gov.ar:11336/198380instacron: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 13:14:34.464CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Classification of 7-dimensional einstein nilradicals
title Classification of 7-dimensional einstein nilradicals
spellingShingle Classification of 7-dimensional einstein nilradicals
Fernández Culma, Edison Alberto
EINSTEIN MANIFOLDS
EINSTEIN NILRADICAL
NILSOLITONS
GEOMETRIC INVARIANT THEORY
title_short Classification of 7-dimensional einstein nilradicals
title_full Classification of 7-dimensional einstein nilradicals
title_fullStr Classification of 7-dimensional einstein nilradicals
title_full_unstemmed Classification of 7-dimensional einstein nilradicals
title_sort Classification of 7-dimensional einstein nilradicals
dc.creator.none.fl_str_mv Fernández Culma, Edison Alberto
author Fernández Culma, Edison Alberto
author_facet Fernández Culma, Edison Alberto
author_role author
dc.subject.none.fl_str_mv EINSTEIN MANIFOLDS
EINSTEIN NILRADICAL
NILSOLITONS
GEOMETRIC INVARIANT THEORY
topic EINSTEIN MANIFOLDS
EINSTEIN NILRADICAL
NILSOLITONS
GEOMETRIC INVARIANT THEORY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The problem of classifying Einstein solvmanifolds, or equivalently, Ricci soliton nilmanifolds, is known to be equivalent to a question on the variety N n(ℂ) of n-dimensional complex nilpotent Lie algebra laws. Namely, one has to determine which GL n(ℂ)-orbits in N n(ℂ) have a critical point of the squared norm of the moment map. In this paper, we give a classification result of such distinguished orbits for n = 7. The set N 7(ℂ)/GL 7(ℂ) is formed by 148 nilpotent Lie algebras and 6 one-parameter families of pairwise non-isomorphic nilpotent Lie algebras. We have applied to each Lie algebra one of three main techniques to decide whether it has a distinguished orbit or not.
Fil: Fernández Culma, Edison Alberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; 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 The problem of classifying Einstein solvmanifolds, or equivalently, Ricci soliton nilmanifolds, is known to be equivalent to a question on the variety N n(ℂ) of n-dimensional complex nilpotent Lie algebra laws. Namely, one has to determine which GL n(ℂ)-orbits in N n(ℂ) have a critical point of the squared norm of the moment map. In this paper, we give a classification result of such distinguished orbits for n = 7. The set N 7(ℂ)/GL 7(ℂ) is formed by 148 nilpotent Lie algebras and 6 one-parameter families of pairwise non-isomorphic nilpotent Lie algebras. We have applied to each Lie algebra one of three main techniques to decide whether it has a distinguished orbit or not.
publishDate 2012
dc.date.none.fl_str_mv 2012-08
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/11336/198380
Fernández Culma, Edison Alberto; Classification of 7-dimensional einstein nilradicals; Birkhauser Boston Inc; Transformation Groups; 17; 3; 8-2012; 639-656
1083-4362
1531-586X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/198380
identifier_str_mv Fernández Culma, Edison Alberto; Classification of 7-dimensional einstein nilradicals; Birkhauser Boston Inc; Transformation Groups; 17; 3; 8-2012; 639-656
1083-4362
1531-586X
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://link.springer.com/article/10.1007%2Fs00031-012-9186-5
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00031-012-9186-5
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 Birkhauser Boston Inc
publisher.none.fl_str_mv Birkhauser Boston Inc
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_ 1842980779334828032
score 12.993085

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