On the structure group of an infinite dimensional JB-algebra

Autores
Larotonda, Gabriel Andrés; Luna, Jose Alejandro
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We extend several results for the structure group of a real Jordan algebra V, to the setting of infinite dimensional JB-algebras. We prove that the structure group Str(V), the cone preserving group G(Ω) and the automorphism group Aut(V) of the algebra V are embedded Banach-Lie groups of GL(V), and that each of the inclusions Aut(V)⊂G(Ω)⊂Str(V) are of embedded Banach-Lie subgroups. We give a full description of the components of Str(V) via cones, isotopes and central projections. We apply these results to V=B(H)sa the special JB-algebra of self-adjoint operators on an infinite dimensional complex Hilbert space, describing the groups Str(V),G(Ω),Aut(V), their Banach-Lie algebras and their connected components. We show that the action of the unitary group of H on Aut(V) has smooth local cross sections, thus Aut(V) is a smooth principal bundle over the unitary group, with circle structure group S1.
Fil: Larotonda, Gabriel Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas; 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
Materia
AUTOMORPHISM GROUP
BANACH-LIE GROUP
JB-ALGEBRA
JORDAN ALGEBRA
QUADRATIC REPRESENTATION
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:11336/212088
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling On the structure group of an infinite dimensional JB-algebraLarotonda, Gabriel AndrésLuna, Jose AlejandroAUTOMORPHISM GROUPBANACH-LIE GROUPJB-ALGEBRAJORDAN ALGEBRAQUADRATIC REPRESENTATIONSTRUCTURE GROUPhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We extend several results for the structure group of a real Jordan algebra V, to the setting of infinite dimensional JB-algebras. We prove that the structure group Str(V), the cone preserving group G(Ω) and the automorphism group Aut(V) of the algebra V are embedded Banach-Lie groups of GL(V), and that each of the inclusions Aut(V)⊂G(Ω)⊂Str(V) are of embedded Banach-Lie subgroups. We give a full description of the components of Str(V) via cones, isotopes and central projections. We apply these results to V=B(H)sa the special JB-algebra of self-adjoint operators on an infinite dimensional complex Hilbert space, describing the groups Str(V),G(Ω),Aut(V), their Banach-Lie algebras and their connected components. We show that the action of the unitary group of H on Aut(V) has smooth local cross sections, thus Aut(V) is a smooth principal bundle over the unitary group, with circle structure group S1.Fil: Larotonda, Gabriel Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas; 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; ArgentinaAcademic Press Inc Elsevier Science2023-05info: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/11336/212088Larotonda, Gabriel Andrés; Luna, Jose Alejandro; On the structure group of an infinite dimensional JB-algebra; Academic Press Inc Elsevier Science; Journal of Algebra; 622; 5-2023; 366-4030021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2023.02.003info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0021869323000509info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2206.05320info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:46:01Zoai:ri.conicet.gov.ar:11336/212088instacron: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:34982025-10-22 11:46:01.302CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the structure group of an infinite dimensional JB-algebra
title On the structure group of an infinite dimensional JB-algebra
spellingShingle On the structure group of an infinite dimensional JB-algebra
Larotonda, Gabriel Andrés
AUTOMORPHISM GROUP
BANACH-LIE GROUP
JB-ALGEBRA
JORDAN ALGEBRA
QUADRATIC REPRESENTATION
STRUCTURE GROUP
title_short On the structure group of an infinite dimensional JB-algebra
title_full On the structure group of an infinite dimensional JB-algebra
title_fullStr On the structure group of an infinite dimensional JB-algebra
title_full_unstemmed On the structure group of an infinite dimensional JB-algebra
title_sort On the structure group of an infinite dimensional 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
JB-ALGEBRA
JORDAN ALGEBRA
QUADRATIC REPRESENTATION
STRUCTURE GROUP
topic AUTOMORPHISM GROUP
BANACH-LIE GROUP
JB-ALGEBRA
JORDAN ALGEBRA
QUADRATIC REPRESENTATION
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 extend several results for the structure group of a real Jordan algebra V, to the setting of infinite dimensional JB-algebras. We prove that the structure group Str(V), the cone preserving group G(Ω) and the automorphism group Aut(V) of the algebra V are embedded Banach-Lie groups of GL(V), and that each of the inclusions Aut(V)⊂G(Ω)⊂Str(V) are of embedded Banach-Lie subgroups. We give a full description of the components of Str(V) via cones, isotopes and central projections. We apply these results to V=B(H)sa the special JB-algebra of self-adjoint operators on an infinite dimensional complex Hilbert space, describing the groups Str(V),G(Ω),Aut(V), their Banach-Lie algebras and their connected components. We show that the action of the unitary group of H on Aut(V) has smooth local cross sections, thus Aut(V) is a smooth principal bundle over the unitary group, with circle structure group S1.
Fil: Larotonda, Gabriel Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas; 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
description We extend several results for the structure group of a real Jordan algebra V, to the setting of infinite dimensional JB-algebras. We prove that the structure group Str(V), the cone preserving group G(Ω) and the automorphism group Aut(V) of the algebra V are embedded Banach-Lie groups of GL(V), and that each of the inclusions Aut(V)⊂G(Ω)⊂Str(V) are of embedded Banach-Lie subgroups. We give a full description of the components of Str(V) via cones, isotopes and central projections. We apply these results to V=B(H)sa the special JB-algebra of self-adjoint operators on an infinite dimensional complex Hilbert space, describing the groups Str(V),G(Ω),Aut(V), their Banach-Lie algebras and their connected components. We show that the action of the unitary group of H on Aut(V) has smooth local cross sections, thus Aut(V) is a smooth principal bundle over the unitary group, with circle structure group S1.
publishDate 2023
dc.date.none.fl_str_mv 2023-05
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/11336/212088
Larotonda, Gabriel Andrés; Luna, Jose Alejandro; On the structure group of an infinite dimensional JB-algebra; Academic Press Inc Elsevier Science; Journal of Algebra; 622; 5-2023; 366-403
0021-8693
CONICET Digital
CONICET
url http://hdl.handle.net/11336/212088
identifier_str_mv Larotonda, Gabriel Andrés; Luna, Jose Alejandro; On the structure group of an infinite dimensional JB-algebra; Academic Press Inc Elsevier Science; Journal of Algebra; 622; 5-2023; 366-403
0021-8693
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.jalgebra.2023.02.003
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0021869323000509
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2206.05320
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 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 12.982451

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