Connections and Finsler geometry of the structure group of a JB-algebra

Autores
Larotonda, Gabriel Andrés; Luna, Jose Alejandro
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We endow the Banach-Lie structure group Str(V) of an infinite dimensional JB-algebra V with a left-invariant connection and Finsler metric, and wecompute all the quantities of its connection. We show how this connection reduces toG(Ω), the group of transformations that preserve the positive cone Ω of the algebraV , and to Aut(V ), the group of Jordan automorphisms of the algebra. We presentthe cone Ω as a homogeneous space for the action of G(Ω), therefore inducing aquotient Finsler metric and distance. With the techniques introduced, we prove theminimality of the one-parameter groups in Ω for any symmetric gauge norm in V .We establish that the two presentations of the Finsler metric in Ω give the samedistance there, which helps us prove the minimality of certain paths in G(Ω) for itsleft-invariant Finsler metric.
Fil: Larotonda, Gabriel Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Luna, Jose Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
AUTOMORPHISM GROUP
BANACH-LIE GROUP
BI-INVARIANT METRIC
CONE
CONNECTION
DISTANCE
FINSLER
GEODESIC
HOMOGENEOUS SPACE
JORDAN ALGEBRA
JB-ALGEBRA
METRIC
ONE PARAMETER GROUP
QUOTIENT METRIC
STRUCTURE 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:11336/266947
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/266947
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Connections and Finsler geometry of the structure group of a JB-algebraLarotonda, Gabriel AndrésLuna, Jose AlejandroAUTOMORPHISM GROUPBANACH-LIE GROUPBI-INVARIANT METRICCONECONNECTIONDISTANCEFINSLERGEODESICHOMOGENEOUS SPACEJORDAN ALGEBRAJB-ALGEBRAMETRICONE PARAMETER GROUPQUOTIENT METRICSTRUCTURE GROUPhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We endow the Banach-Lie structure group Str(V) of an infinite dimensional JB-algebra V with a left-invariant connection and Finsler metric, and wecompute all the quantities of its connection. We show how this connection reduces toG(Ω), the group of transformations that preserve the positive cone Ω of the algebraV , and to Aut(V ), the group of Jordan automorphisms of the algebra. We presentthe cone Ω as a homogeneous space for the action of G(Ω), therefore inducing aquotient Finsler metric and distance. With the techniques introduced, we prove theminimality of the one-parameter groups in Ω for any symmetric gauge norm in V .We establish that the two presentations of the Finsler metric in Ω give the samedistance there, which helps us prove the minimality of certain paths in G(Ω) for itsleft-invariant Finsler metric.Fil: Larotonda, Gabriel Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Luna, Jose Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaAcademic Press Inc Elsevier Science2025-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/266947Larotonda, Gabriel Andrés; Luna, Jose Alejandro; Connections and Finsler geometry of the structure group of a JB-algebra; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 550; 1; 3-2025; 1-30, 1295060022-247XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2025.129506info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0022247X25002872?via%3Dihubinfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/html/2206.09208v3info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:36:35Zoai:ri.conicet.gov.ar:11336/266947instacron: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 14:36:35.473CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Connections and Finsler geometry of the structure group of a JB-algebra
title Connections and Finsler geometry of the structure group of a JB-algebra
spellingShingle Connections and Finsler geometry of the structure group of a JB-algebra
Larotonda, Gabriel Andrés
AUTOMORPHISM GROUP
BANACH-LIE GROUP
BI-INVARIANT METRIC
CONE
CONNECTION
DISTANCE
FINSLER
GEODESIC
HOMOGENEOUS SPACE
JORDAN ALGEBRA
JB-ALGEBRA
METRIC
ONE PARAMETER GROUP
QUOTIENT METRIC
STRUCTURE GROUP
title_short Connections and Finsler geometry of the structure group of a JB-algebra
title_full Connections and Finsler geometry of the structure group of a JB-algebra
title_fullStr Connections and Finsler geometry of the structure group of a JB-algebra
title_full_unstemmed Connections and Finsler geometry of the structure group of a JB-algebra
title_sort Connections and Finsler geometry of the structure group of a JB-algebra
dc.creator.none.fl_str_mv Larotonda, Gabriel Andrés
Luna, Jose Alejandro
author Larotonda, Gabriel Andrés
author_facet Larotonda, Gabriel Andrés
Luna, Jose Alejandro
author_role author
author2 Luna, Jose Alejandro
author2_role author
dc.subject.none.fl_str_mv AUTOMORPHISM GROUP
BANACH-LIE GROUP
BI-INVARIANT METRIC
CONE
CONNECTION
DISTANCE
FINSLER
GEODESIC
HOMOGENEOUS SPACE
JORDAN ALGEBRA
JB-ALGEBRA
METRIC
ONE PARAMETER GROUP
QUOTIENT METRIC
STRUCTURE GROUP
topic AUTOMORPHISM GROUP
BANACH-LIE GROUP
BI-INVARIANT METRIC
CONE
CONNECTION
DISTANCE
FINSLER
GEODESIC
HOMOGENEOUS SPACE
JORDAN ALGEBRA
JB-ALGEBRA
METRIC
ONE PARAMETER GROUP
QUOTIENT METRIC
STRUCTURE 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 endow the Banach-Lie structure group Str(V) of an infinite dimensional JB-algebra V with a left-invariant connection and Finsler metric, and wecompute all the quantities of its connection. We show how this connection reduces toG(Ω), the group of transformations that preserve the positive cone Ω of the algebraV , and to Aut(V ), the group of Jordan automorphisms of the algebra. We presentthe cone Ω as a homogeneous space for the action of G(Ω), therefore inducing aquotient Finsler metric and distance. With the techniques introduced, we prove theminimality of the one-parameter groups in Ω for any symmetric gauge norm in V .We establish that the two presentations of the Finsler metric in Ω give the samedistance there, which helps us prove the minimality of certain paths in G(Ω) for itsleft-invariant Finsler metric.
Fil: Larotonda, Gabriel Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Luna, Jose Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description We endow the Banach-Lie structure group Str(V) of an infinite dimensional JB-algebra V with a left-invariant connection and Finsler metric, and wecompute all the quantities of its connection. We show how this connection reduces toG(Ω), the group of transformations that preserve the positive cone Ω of the algebraV , and to Aut(V ), the group of Jordan automorphisms of the algebra. We presentthe cone Ω as a homogeneous space for the action of G(Ω), therefore inducing aquotient Finsler metric and distance. With the techniques introduced, we prove theminimality of the one-parameter groups in Ω for any symmetric gauge norm in V .We establish that the two presentations of the Finsler metric in Ω give the samedistance there, which helps us prove the minimality of certain paths in G(Ω) for itsleft-invariant Finsler metric.
publishDate 2025
dc.date.none.fl_str_mv 2025-03
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/11336/266947
Larotonda, Gabriel Andrés; Luna, Jose Alejandro; Connections and Finsler geometry of the structure group of a JB-algebra; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 550; 1; 3-2025; 1-30, 129506
0022-247X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/266947
identifier_str_mv Larotonda, Gabriel Andrés; Luna, Jose Alejandro; Connections and Finsler geometry of the structure group of a JB-algebra; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 550; 1; 3-2025; 1-30, 129506
0022-247X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2025.129506
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0022247X25002872?via%3Dihub
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/html/2206.09208v3
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
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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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