Metric geometry of infinite dimensional Lie groups and their homogeneous spaces

Autores
Larotonda, Gabriel Andrés
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the geometry of Lie groups G with a continuous Finsler metric, in presence of a subgroup K such that the metric is right-invariant for the action of K. We present a systematic study of the metric and geodesic structure of homogeneous spaces M obtained by the quotient M≃G/K. Of particular interest are left-invariant metrics of G which are then bi-invariant for the action of K. We then focus on the geodesic structure of groups K that admit bi-invariant metrics, proving that one-parameter groups are short paths for those metrics, and characterizing all other short paths. We provide applications of the results obtained, in two settings: manifolds of Banach space linear operators, and groups of maps from compact manifolds.
Fil: Larotonda, Gabriel Andrés. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
LIE GROUP
BANACH SPACE
FINSLER METRIC
HOMOGENEOUS SPACE
QUOTIENT METRIC
BI-INVARIANT METRIC
GEODESIC
ONE-PARAMETER GROUP
DIFFEOMORPHISM GROUP
LOOP GROUP
OPERATOR ALGEBRA
OPERATOR IDEAL
UNITARY GROUP
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:11336/107581
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/107581
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Metric geometry of infinite dimensional Lie groups and their homogeneous spacesLarotonda, Gabriel AndrésLIE GROUPBANACH SPACEFINSLER METRICHOMOGENEOUS SPACEQUOTIENT METRICBI-INVARIANT METRICGEODESICONE-PARAMETER GROUPDIFFEOMORPHISM GROUPLOOP GROUPOPERATOR ALGEBRAOPERATOR IDEALUNITARY GROUPhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the geometry of Lie groups G with a continuous Finsler metric, in presence of a subgroup K such that the metric is right-invariant for the action of K. We present a systematic study of the metric and geodesic structure of homogeneous spaces M obtained by the quotient M≃G/K. Of particular interest are left-invariant metrics of G which are then bi-invariant for the action of K. We then focus on the geodesic structure of groups K that admit bi-invariant metrics, proving that one-parameter groups are short paths for those metrics, and characterizing all other short paths. We provide applications of the results obtained, in two settings: manifolds of Banach space linear operators, and groups of maps from compact manifolds.Fil: Larotonda, Gabriel Andrés. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaDe Gruyter2019-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/107581Larotonda, Gabriel Andrés; Metric geometry of infinite dimensional Lie groups and their homogeneous spaces; De Gruyter; Forum Mathematicum; 31; 6; 9-2019; 1567-16050933-77411435-5337CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/journals/form/31/6/article-p1567.xmlinfo:eu-repo/semantics/altIdentifier/doi/10.1515/forum-2019-0127info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1805.02631info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-26T09:05:48Zoai:ri.conicet.gov.ar:11336/107581instacron: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:34982025-11-26 09:05:48.902CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Metric geometry of infinite dimensional Lie groups and their homogeneous spaces
title Metric geometry of infinite dimensional Lie groups and their homogeneous spaces
spellingShingle Metric geometry of infinite dimensional Lie groups and their homogeneous spaces
Larotonda, Gabriel Andrés
LIE GROUP
BANACH SPACE
FINSLER METRIC
HOMOGENEOUS SPACE
QUOTIENT METRIC
BI-INVARIANT METRIC
GEODESIC
ONE-PARAMETER GROUP
DIFFEOMORPHISM GROUP
LOOP GROUP
OPERATOR ALGEBRA
OPERATOR IDEAL
UNITARY GROUP
title_short Metric geometry of infinite dimensional Lie groups and their homogeneous spaces
title_full Metric geometry of infinite dimensional Lie groups and their homogeneous spaces
title_fullStr Metric geometry of infinite dimensional Lie groups and their homogeneous spaces
title_full_unstemmed Metric geometry of infinite dimensional Lie groups and their homogeneous spaces
title_sort Metric geometry of infinite dimensional Lie groups and their homogeneous spaces
dc.creator.none.fl_str_mv Larotonda, Gabriel Andrés
author Larotonda, Gabriel Andrés
author_facet Larotonda, Gabriel Andrés
author_role author
dc.subject.none.fl_str_mv LIE GROUP
BANACH SPACE
FINSLER METRIC
HOMOGENEOUS SPACE
QUOTIENT METRIC
BI-INVARIANT METRIC
GEODESIC
ONE-PARAMETER GROUP
DIFFEOMORPHISM GROUP
LOOP GROUP
OPERATOR ALGEBRA
OPERATOR IDEAL
UNITARY GROUP
topic LIE GROUP
BANACH SPACE
FINSLER METRIC
HOMOGENEOUS SPACE
QUOTIENT METRIC
BI-INVARIANT METRIC
GEODESIC
ONE-PARAMETER GROUP
DIFFEOMORPHISM GROUP
LOOP GROUP
OPERATOR ALGEBRA
OPERATOR IDEAL
UNITARY GROUP
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study the geometry of Lie groups G with a continuous Finsler metric, in presence of a subgroup K such that the metric is right-invariant for the action of K. We present a systematic study of the metric and geodesic structure of homogeneous spaces M obtained by the quotient M≃G/K. Of particular interest are left-invariant metrics of G which are then bi-invariant for the action of K. We then focus on the geodesic structure of groups K that admit bi-invariant metrics, proving that one-parameter groups are short paths for those metrics, and characterizing all other short paths. We provide applications of the results obtained, in two settings: manifolds of Banach space linear operators, and groups of maps from compact manifolds.
Fil: Larotonda, Gabriel Andrés. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description We study the geometry of Lie groups G with a continuous Finsler metric, in presence of a subgroup K such that the metric is right-invariant for the action of K. We present a systematic study of the metric and geodesic structure of homogeneous spaces M obtained by the quotient M≃G/K. Of particular interest are left-invariant metrics of G which are then bi-invariant for the action of K. We then focus on the geodesic structure of groups K that admit bi-invariant metrics, proving that one-parameter groups are short paths for those metrics, and characterizing all other short paths. We provide applications of the results obtained, in two settings: manifolds of Banach space linear operators, and groups of maps from compact manifolds.
publishDate 2019
dc.date.none.fl_str_mv 2019-09
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/11336/107581
Larotonda, Gabriel Andrés; Metric geometry of infinite dimensional Lie groups and their homogeneous spaces; De Gruyter; Forum Mathematicum; 31; 6; 9-2019; 1567-1605
0933-7741
1435-5337
CONICET Digital
CONICET
url http://hdl.handle.net/11336/107581
identifier_str_mv Larotonda, Gabriel Andrés; Metric geometry of infinite dimensional Lie groups and their homogeneous spaces; De Gruyter; Forum Mathematicum; 31; 6; 9-2019; 1567-1605
0933-7741
1435-5337
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://www.degruyter.com/view/journals/form/31/6/article-p1567.xml
info:eu-repo/semantics/altIdentifier/doi/10.1515/forum-2019-0127
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1805.02631
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
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 13.011256

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