On Ricci negative derivations

Autores
Gutiérrez, María Valeria
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given a nilpotent Lie algebra, we study the space of all diagonalizable derivations such that the corresponding one-dimensional solvable extension admits a left-invariant metric with negative Ricci curvature. Lauret and Will have conjectured that such a space coincides with an open and convex subset of derivations defined in terms of the moment map for the variety of nilpotent Lie algebras. We prove the validity of the conjecture in dimensions ≤ 5, as well as for Heisenberg Lie algebras and standard filiform Lie algebras.
Fil: Gutiérrez, María Valeria. Universidad Nacional de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Materia
FILIFORM LIE ALGEBRA
HEISENBERG LIE ALGEBRA
NEGATIVE RICCI CURVATURE
SOLVABLE LIE ALGEBRA
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:11336/219077
Acceder
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network_name_str CONICET Digital (CONICET)
spelling On Ricci negative derivationsGutiérrez, María ValeriaFILIFORM LIE ALGEBRAHEISENBERG LIE ALGEBRANEGATIVE RICCI CURVATURESOLVABLE LIE ALGEBRAhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given a nilpotent Lie algebra, we study the space of all diagonalizable derivations such that the corresponding one-dimensional solvable extension admits a left-invariant metric with negative Ricci curvature. Lauret and Will have conjectured that such a space coincides with an open and convex subset of derivations defined in terms of the moment map for the variety of nilpotent Lie algebras. We prove the validity of the conjecture in dimensions ≤ 5, as well as for Heisenberg Lie algebras and standard filiform Lie algebras.Fil: Gutiérrez, María Valeria. Universidad Nacional de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaDe Gruyter2022-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/219077Gutiérrez, María Valeria; On Ricci negative derivations; De Gruyter; Advances In Geometry; 22; 2; 4-2022; 199-2141615-715XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1515/advgeom-2022-0004info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/document/doi/10.1515/advgeom-2022-0004/htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:05:00Zoai:ri.conicet.gov.ar:11336/219077instacron: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 10:05:00.744CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On Ricci negative derivations
title On Ricci negative derivations
spellingShingle On Ricci negative derivations
Gutiérrez, María Valeria
FILIFORM LIE ALGEBRA
HEISENBERG LIE ALGEBRA
NEGATIVE RICCI CURVATURE
SOLVABLE LIE ALGEBRA
title_short On Ricci negative derivations
title_full On Ricci negative derivations
title_fullStr On Ricci negative derivations
title_full_unstemmed On Ricci negative derivations
title_sort On Ricci negative derivations
dc.creator.none.fl_str_mv Gutiérrez, María Valeria
author Gutiérrez, María Valeria
author_facet Gutiérrez, María Valeria
author_role author
dc.subject.none.fl_str_mv FILIFORM LIE ALGEBRA
HEISENBERG LIE ALGEBRA
NEGATIVE RICCI CURVATURE
SOLVABLE LIE ALGEBRA
topic FILIFORM LIE ALGEBRA
HEISENBERG LIE ALGEBRA
NEGATIVE RICCI CURVATURE
SOLVABLE LIE ALGEBRA
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Given a nilpotent Lie algebra, we study the space of all diagonalizable derivations such that the corresponding one-dimensional solvable extension admits a left-invariant metric with negative Ricci curvature. Lauret and Will have conjectured that such a space coincides with an open and convex subset of derivations defined in terms of the moment map for the variety of nilpotent Lie algebras. We prove the validity of the conjecture in dimensions ≤ 5, as well as for Heisenberg Lie algebras and standard filiform Lie algebras.
Fil: Gutiérrez, María Valeria. Universidad Nacional de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
description Given a nilpotent Lie algebra, we study the space of all diagonalizable derivations such that the corresponding one-dimensional solvable extension admits a left-invariant metric with negative Ricci curvature. Lauret and Will have conjectured that such a space coincides with an open and convex subset of derivations defined in terms of the moment map for the variety of nilpotent Lie algebras. We prove the validity of the conjecture in dimensions ≤ 5, as well as for Heisenberg Lie algebras and standard filiform Lie algebras.
publishDate 2022
dc.date.none.fl_str_mv 2022-04
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/11336/219077
Gutiérrez, María Valeria; On Ricci negative derivations; De Gruyter; Advances In Geometry; 22; 2; 4-2022; 199-214
1615-715X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/219077
identifier_str_mv Gutiérrez, María Valeria; On Ricci negative derivations; De Gruyter; Advances In Geometry; 22; 2; 4-2022; 199-214
1615-715X
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/advgeom-2022-0004
info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/document/doi/10.1515/advgeom-2022-0004/html
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 13.13397

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