Classification of 6-dimensional splittable flat solvmanifolds

Autores
Tolcachier, Alejandro
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A flat solvmanifold is a compact quotient Γ∖G where G is a simply-connected solvable Lie group endowed with a flat left invariant metric and Γ is a lattice of G. Any such Lie group can be written as G=Rk ltimes_ϕ Rm with Rm the nilradical. In this article we focus on 6-dimensional splittable flat solvmanifolds, which are obtained quotienting G by a lattice Γ that can be decomposed as Γ=Γ1 ltimes_ϕ Γ2, where Γ1 and Γ2 are lattices of Rk and Rm, respectively. We analyze the relation between these lattices and the conjugacy classes of finite abelian subgroups of GL(n,Z), which is known up to n≤6. From this we obtain the classification of 6-dimensional splittable flat solvmanifolds.
Fil: Tolcachier, Alejandro. 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
Splittable Lie group
Flat manifold
Solvmanifold
Lattice
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:11336/215085
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Classification of 6-dimensional splittable flat solvmanifoldsTolcachier, AlejandroSplittable Lie groupFlat manifoldSolvmanifoldLatticehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A flat solvmanifold is a compact quotient Γ∖G where G is a simply-connected solvable Lie group endowed with a flat left invariant metric and Γ is a lattice of G. Any such Lie group can be written as G=Rk ltimes_ϕ Rm with Rm the nilradical. In this article we focus on 6-dimensional splittable flat solvmanifolds, which are obtained quotienting G by a lattice Γ that can be decomposed as Γ=Γ1 ltimes_ϕ Γ2, where Γ1 and Γ2 are lattices of Rk and Rm, respectively. We analyze the relation between these lattices and the conjugacy classes of finite abelian subgroups of GL(n,Z), which is known up to n≤6. From this we obtain the classification of 6-dimensional splittable flat solvmanifolds.Fil: Tolcachier, Alejandro. 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; ArgentinaSpringer2022-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/215085Tolcachier, Alejandro; Classification of 6-dimensional splittable flat solvmanifolds; Springer; Manuscripta Mathematica; 1-2022; 1-310025-2611CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00229-021-01364-winfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00229-021-01364-winfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:42:31Zoai:ri.conicet.gov.ar:11336/215085instacron: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 15:42:31.873CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Classification of 6-dimensional splittable flat solvmanifolds
title Classification of 6-dimensional splittable flat solvmanifolds
spellingShingle Classification of 6-dimensional splittable flat solvmanifolds
Tolcachier, Alejandro
Splittable Lie group
Flat manifold
Solvmanifold
Lattice
title_short Classification of 6-dimensional splittable flat solvmanifolds
title_full Classification of 6-dimensional splittable flat solvmanifolds
title_fullStr Classification of 6-dimensional splittable flat solvmanifolds
title_full_unstemmed Classification of 6-dimensional splittable flat solvmanifolds
title_sort Classification of 6-dimensional splittable flat solvmanifolds
dc.creator.none.fl_str_mv Tolcachier, Alejandro
author Tolcachier, Alejandro
author_facet Tolcachier, Alejandro
author_role author
dc.subject.none.fl_str_mv Splittable Lie group
Flat manifold
Solvmanifold
Lattice
topic Splittable Lie group
Flat manifold
Solvmanifold
Lattice
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 flat solvmanifold is a compact quotient Γ∖G where G is a simply-connected solvable Lie group endowed with a flat left invariant metric and Γ is a lattice of G. Any such Lie group can be written as G=Rk ltimes_ϕ Rm with Rm the nilradical. In this article we focus on 6-dimensional splittable flat solvmanifolds, which are obtained quotienting G by a lattice Γ that can be decomposed as Γ=Γ1 ltimes_ϕ Γ2, where Γ1 and Γ2 are lattices of Rk and Rm, respectively. We analyze the relation between these lattices and the conjugacy classes of finite abelian subgroups of GL(n,Z), which is known up to n≤6. From this we obtain the classification of 6-dimensional splittable flat solvmanifolds.
Fil: Tolcachier, Alejandro. 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 A flat solvmanifold is a compact quotient Γ∖G where G is a simply-connected solvable Lie group endowed with a flat left invariant metric and Γ is a lattice of G. Any such Lie group can be written as G=Rk ltimes_ϕ Rm with Rm the nilradical. In this article we focus on 6-dimensional splittable flat solvmanifolds, which are obtained quotienting G by a lattice Γ that can be decomposed as Γ=Γ1 ltimes_ϕ Γ2, where Γ1 and Γ2 are lattices of Rk and Rm, respectively. We analyze the relation between these lattices and the conjugacy classes of finite abelian subgroups of GL(n,Z), which is known up to n≤6. From this we obtain the classification of 6-dimensional splittable flat solvmanifolds.
publishDate 2022
dc.date.none.fl_str_mv 2022-01
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/11336/215085
Tolcachier, Alejandro; Classification of 6-dimensional splittable flat solvmanifolds; Springer; Manuscripta Mathematica; 1-2022; 1-31
0025-2611
CONICET Digital
CONICET
url http://hdl.handle.net/11336/215085
identifier_str_mv Tolcachier, Alejandro; Classification of 6-dimensional splittable flat solvmanifolds; Springer; Manuscripta Mathematica; 1-2022; 1-31
0025-2611
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00229-021-01364-w
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00229-021-01364-w
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 Springer
publisher.none.fl_str_mv Springer
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 13.22299

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