The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds

Autores
Cardoso, Isolda Eugenia; Cosgaya, Ana; Reggiani, Silvio Nicolás
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A real Lie algebra is said to be characteristically solvable if its derivation algebra is solvable. We explicitly determine the moduli space of left-invariant metrics, up to isometric automorphism, for 6-dimensional nilmanifolds whose associated Lie algebra is characteristically solvable. We also compute the corresponding full isometry groups. For each left-invariant metric on these nilmanifolds we compute the index and distribution of symmetry. In particular, we find the first known examples of Lie groups which do not admit a left-invariant metric with positive index of symmetry. As an application we study the index of symmetry of nilsoliton metrics on characteristically solvable Lie algebras. We prove that nilsoliton metrics detect the existence of left-invariant metrics with positive index of symmetry.
Fil: Cardoso, Isolda Eugenia. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Cosgaya, Ana. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Reggiani, Silvio Nicolás. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Materia
CHARACTERISTICALLY SOLVABLE LIE ALGEBRA
NILMANIFOLD
LEFT-INVARIANT METRIC
INDEX OF SYMMETRY
DISTRIBUTION OF SYMMETRY
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:11336/239698
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifoldsCardoso, Isolda EugeniaCosgaya, AnaReggiani, Silvio NicolásCHARACTERISTICALLY SOLVABLE LIE ALGEBRANILMANIFOLDLEFT-INVARIANT METRICINDEX OF SYMMETRYDISTRIBUTION OF SYMMETRYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A real Lie algebra is said to be characteristically solvable if its derivation algebra is solvable. We explicitly determine the moduli space of left-invariant metrics, up to isometric automorphism, for 6-dimensional nilmanifolds whose associated Lie algebra is characteristically solvable. We also compute the corresponding full isometry groups. For each left-invariant metric on these nilmanifolds we compute the index and distribution of symmetry. In particular, we find the first known examples of Lie groups which do not admit a left-invariant metric with positive index of symmetry. As an application we study the index of symmetry of nilsoliton metrics on characteristically solvable Lie algebras. We prove that nilsoliton metrics detect the existence of left-invariant metrics with positive index of symmetry.Fil: Cardoso, Isolda Eugenia. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Cosgaya, Ana. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Reggiani, Silvio Nicolás. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaCornell University2024-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/239698Cardoso, Isolda Eugenia; Cosgaya, Ana; Reggiani, Silvio Nicolás; The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds; Cornell University; ArXiv.org; 2024; 5-2024; 1-242331-8422CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2404.19177info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2404.19177info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:38:06Zoai:ri.conicet.gov.ar:11336/239698instacron: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:34982025-10-15 14:38:07.149CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds
title The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds
spellingShingle The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds
Cardoso, Isolda Eugenia
CHARACTERISTICALLY SOLVABLE LIE ALGEBRA
NILMANIFOLD
LEFT-INVARIANT METRIC
INDEX OF SYMMETRY
DISTRIBUTION OF SYMMETRY
title_short The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds
title_full The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds
title_fullStr The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds
title_full_unstemmed The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds
title_sort The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds
dc.creator.none.fl_str_mv Cardoso, Isolda Eugenia
Cosgaya, Ana
Reggiani, Silvio Nicolás
author Cardoso, Isolda Eugenia
author_facet Cardoso, Isolda Eugenia
Cosgaya, Ana
Reggiani, Silvio Nicolás
author_role author
author2 Cosgaya, Ana
Reggiani, Silvio Nicolás
author2_role author
author
dc.subject.none.fl_str_mv CHARACTERISTICALLY SOLVABLE LIE ALGEBRA
NILMANIFOLD
LEFT-INVARIANT METRIC
INDEX OF SYMMETRY
DISTRIBUTION OF SYMMETRY
topic CHARACTERISTICALLY SOLVABLE LIE ALGEBRA
NILMANIFOLD
LEFT-INVARIANT METRIC
INDEX OF SYMMETRY
DISTRIBUTION OF SYMMETRY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A real Lie algebra is said to be characteristically solvable if its derivation algebra is solvable. We explicitly determine the moduli space of left-invariant metrics, up to isometric automorphism, for 6-dimensional nilmanifolds whose associated Lie algebra is characteristically solvable. We also compute the corresponding full isometry groups. For each left-invariant metric on these nilmanifolds we compute the index and distribution of symmetry. In particular, we find the first known examples of Lie groups which do not admit a left-invariant metric with positive index of symmetry. As an application we study the index of symmetry of nilsoliton metrics on characteristically solvable Lie algebras. We prove that nilsoliton metrics detect the existence of left-invariant metrics with positive index of symmetry.
Fil: Cardoso, Isolda Eugenia. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Cosgaya, Ana. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Reggiani, Silvio Nicolás. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
description A real Lie algebra is said to be characteristically solvable if its derivation algebra is solvable. We explicitly determine the moduli space of left-invariant metrics, up to isometric automorphism, for 6-dimensional nilmanifolds whose associated Lie algebra is characteristically solvable. We also compute the corresponding full isometry groups. For each left-invariant metric on these nilmanifolds we compute the index and distribution of symmetry. In particular, we find the first known examples of Lie groups which do not admit a left-invariant metric with positive index of symmetry. As an application we study the index of symmetry of nilsoliton metrics on characteristically solvable Lie algebras. We prove that nilsoliton metrics detect the existence of left-invariant metrics with positive index of symmetry.
publishDate 2024
dc.date.none.fl_str_mv 2024-05
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/11336/239698
Cardoso, Isolda Eugenia; Cosgaya, Ana; Reggiani, Silvio Nicolás; The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds; Cornell University; ArXiv.org; 2024; 5-2024; 1-24
2331-8422
CONICET Digital
CONICET
url http://hdl.handle.net/11336/239698
identifier_str_mv Cardoso, Isolda Eugenia; Cosgaya, Ana; Reggiani, Silvio Nicolás; The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds; Cornell University; ArXiv.org; 2024; 5-2024; 1-24
2331-8422
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://arxiv.org/abs/2404.19177
info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2404.19177
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 Cornell University
publisher.none.fl_str_mv Cornell University
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_ 1846082858525917184
score 13.22299

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