Non-solvable Lie groups with negative Ricci curvature

Autores
Lauret, Emilio Agustin; Will, Cynthia Eugenia
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Until a couple of years ago, the only known examples of Lie groups admitting left-invariant metrics with negative Ricci curvature were either solvable or semisimple.We use a general construction from a previous article of the second named author to produce a large number of examples with compact Levi factor. Given a compact semisimple real Lie algebra u and a real representation π satisfying some technical properties, the construction returns a metric Lie algebra (u,π) with negative Ricci operator. In this paper, when u is assumed to be simple, we prove that (u,π) admits a metric having negative Ricci curvature for all but finitely many finite-dimensional irreducible representations of (Formula presented.), regarded as a real representation of u. We also prove in the last section a more general result where the nilradical is not abelian, as it is in every (u,π).
Fil: Lauret, Emilio Agustin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina. Universidad Nacional del Sur; Argentina
Fil: Will, Cynthia Eugenia. 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. Universidad Nacional de Córdoba; Argentina
Materia
Ricci curvature
Lie algebras
Representations
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:11336/143399
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Non-solvable Lie groups with negative Ricci curvatureLauret, Emilio AgustinWill, Cynthia EugeniaRicci curvatureLie algebrasRepresentationshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Until a couple of years ago, the only known examples of Lie groups admitting left-invariant metrics with negative Ricci curvature were either solvable or semisimple.We use a general construction from a previous article of the second named author to produce a large number of examples with compact Levi factor. Given a compact semisimple real Lie algebra u and a real representation π satisfying some technical properties, the construction returns a metric Lie algebra (u,π) with negative Ricci operator. In this paper, when u is assumed to be simple, we prove that (u,π) admits a metric having negative Ricci curvature for all but finitely many finite-dimensional irreducible representations of (Formula presented.), regarded as a real representation of u. We also prove in the last section a more general result where the nilradical is not abelian, as it is in every (u,π).Fil: Lauret, Emilio Agustin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina. Universidad Nacional del Sur; ArgentinaFil: Will, Cynthia Eugenia. 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. Universidad Nacional de Córdoba; ArgentinaBirkhauser Boston Inc2020-06-16info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/143399Lauret, Emilio Agustin; Will, Cynthia Eugenia; Non-solvable Lie groups with negative Ricci curvature; Birkhauser Boston Inc; Transformation Groups; 16-6-2020; 1-171083-43621531-586XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00031-020-09582-4info:eu-repo/semantics/altIdentifier/doi/10.1007/s00031-020-09582-4info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:06:16Zoai:ri.conicet.gov.ar:11336/143399instacron: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:34982025-09-03 10:06:16.537CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Non-solvable Lie groups with negative Ricci curvature
title Non-solvable Lie groups with negative Ricci curvature
spellingShingle Non-solvable Lie groups with negative Ricci curvature
Lauret, Emilio Agustin
Ricci curvature
Lie algebras
Representations
title_short Non-solvable Lie groups with negative Ricci curvature
title_full Non-solvable Lie groups with negative Ricci curvature
title_fullStr Non-solvable Lie groups with negative Ricci curvature
title_full_unstemmed Non-solvable Lie groups with negative Ricci curvature
title_sort Non-solvable Lie groups with negative Ricci curvature
dc.creator.none.fl_str_mv Lauret, Emilio Agustin
Will, Cynthia Eugenia
author Lauret, Emilio Agustin
author_facet Lauret, Emilio Agustin
Will, Cynthia Eugenia
author_role author
author2 Will, Cynthia Eugenia
author2_role author
dc.subject.none.fl_str_mv Ricci curvature
Lie algebras
Representations
topic Ricci curvature
Lie algebras
Representations
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Until a couple of years ago, the only known examples of Lie groups admitting left-invariant metrics with negative Ricci curvature were either solvable or semisimple.We use a general construction from a previous article of the second named author to produce a large number of examples with compact Levi factor. Given a compact semisimple real Lie algebra u and a real representation π satisfying some technical properties, the construction returns a metric Lie algebra (u,π) with negative Ricci operator. In this paper, when u is assumed to be simple, we prove that (u,π) admits a metric having negative Ricci curvature for all but finitely many finite-dimensional irreducible representations of (Formula presented.), regarded as a real representation of u. We also prove in the last section a more general result where the nilradical is not abelian, as it is in every (u,π).
Fil: Lauret, Emilio Agustin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina. Universidad Nacional del Sur; Argentina
Fil: Will, Cynthia Eugenia. 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. Universidad Nacional de Córdoba; Argentina
description Until a couple of years ago, the only known examples of Lie groups admitting left-invariant metrics with negative Ricci curvature were either solvable or semisimple.We use a general construction from a previous article of the second named author to produce a large number of examples with compact Levi factor. Given a compact semisimple real Lie algebra u and a real representation π satisfying some technical properties, the construction returns a metric Lie algebra (u,π) with negative Ricci operator. In this paper, when u is assumed to be simple, we prove that (u,π) admits a metric having negative Ricci curvature for all but finitely many finite-dimensional irreducible representations of (Formula presented.), regarded as a real representation of u. We also prove in the last section a more general result where the nilradical is not abelian, as it is in every (u,π).
publishDate 2020
dc.date.none.fl_str_mv 2020-06-16
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/11336/143399
Lauret, Emilio Agustin; Will, Cynthia Eugenia; Non-solvable Lie groups with negative Ricci curvature; Birkhauser Boston Inc; Transformation Groups; 16-6-2020; 1-17
1083-4362
1531-586X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/143399
identifier_str_mv Lauret, Emilio Agustin; Will, Cynthia Eugenia; Non-solvable Lie groups with negative Ricci curvature; Birkhauser Boston Inc; Transformation Groups; 16-6-2020; 1-17
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/https://link.springer.com/article/10.1007/s00031-020-09582-4
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00031-020-09582-4
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
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score 13.13397

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