Parabolic subgroups inside parabolic subgroups of Artin groups

Autores
Blufstein, Martín Axel; Paris, Luis
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove that a parabolic subgroup P contained in another parabolic subgroup P of an Artin group A is a parabolic subgroup of P. This answers a question of Godelle which is not obvious despite appearances. In order to achieve our result we construct a set-retraction A → P of the inclusion map from a parabolic subgroup P into A. This retraction was implicitly constructed in a previous paper by Charney and the second author [Bull. Lond. Math. Soc. 46 (2014), pp. 1248–1255].
Fil: Blufstein, Martín Axel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Paris, Luis. Institut de Mathématiques de Bourgogne; Francia
Materia
ARTIN
PARABOLICS
SUBGROUP
RETRACTION
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:11336/228285
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/228285
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Parabolic subgroups inside parabolic subgroups of Artin groupsBlufstein, Martín AxelParis, LuisARTINPARABOLICSSUBGROUPRETRACTIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove that a parabolic subgroup P contained in another parabolic subgroup P of an Artin group A is a parabolic subgroup of P. This answers a question of Godelle which is not obvious despite appearances. In order to achieve our result we construct a set-retraction A → P of the inclusion map from a parabolic subgroup P into A. This retraction was implicitly constructed in a previous paper by Charney and the second author [Bull. Lond. Math. Soc. 46 (2014), pp. 1248–1255].Fil: Blufstein, Martín Axel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Paris, Luis. Institut de Mathématiques de Bourgogne; FranciaAmerican Mathematical Society2023-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/228285Blufstein, Martín Axel; Paris, Luis; Parabolic subgroups inside parabolic subgroups of Artin groups; American Mathematical Society; Proceedings of the American Mathematical Society; 151; 4; 4-2023; 1519-15260002-9939CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1090/proc/16289info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2204.05142info:eu-repo/semantics/altIdentifier/url/https://doi.org/10.48550/arXiv.2204.05142info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:57:40Zoai:ri.conicet.gov.ar:11336/228285instacron: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:34982025-09-03 09:57:41.002CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Parabolic subgroups inside parabolic subgroups of Artin groups
title Parabolic subgroups inside parabolic subgroups of Artin groups
spellingShingle Parabolic subgroups inside parabolic subgroups of Artin groups
Blufstein, Martín Axel
ARTIN
PARABOLICS
SUBGROUP
RETRACTION
title_short Parabolic subgroups inside parabolic subgroups of Artin groups
title_full Parabolic subgroups inside parabolic subgroups of Artin groups
title_fullStr Parabolic subgroups inside parabolic subgroups of Artin groups
title_full_unstemmed Parabolic subgroups inside parabolic subgroups of Artin groups
title_sort Parabolic subgroups inside parabolic subgroups of Artin groups
dc.creator.none.fl_str_mv Blufstein, Martín Axel
Paris, Luis
author Blufstein, Martín Axel
author_facet Blufstein, Martín Axel
Paris, Luis
author_role author
author2 Paris, Luis
author2_role author
dc.subject.none.fl_str_mv ARTIN
PARABOLICS
SUBGROUP
RETRACTION
topic ARTIN
PARABOLICS
SUBGROUP
RETRACTION
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 prove that a parabolic subgroup P contained in another parabolic subgroup P of an Artin group A is a parabolic subgroup of P. This answers a question of Godelle which is not obvious despite appearances. In order to achieve our result we construct a set-retraction A → P of the inclusion map from a parabolic subgroup P into A. This retraction was implicitly constructed in a previous paper by Charney and the second author [Bull. Lond. Math. Soc. 46 (2014), pp. 1248–1255].
Fil: Blufstein, Martín Axel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Paris, Luis. Institut de Mathématiques de Bourgogne; Francia
description We prove that a parabolic subgroup P contained in another parabolic subgroup P of an Artin group A is a parabolic subgroup of P. This answers a question of Godelle which is not obvious despite appearances. In order to achieve our result we construct a set-retraction A → P of the inclusion map from a parabolic subgroup P into A. This retraction was implicitly constructed in a previous paper by Charney and the second author [Bull. Lond. Math. Soc. 46 (2014), pp. 1248–1255].
publishDate 2023
dc.date.none.fl_str_mv 2023-04
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/11336/228285
Blufstein, Martín Axel; Paris, Luis; Parabolic subgroups inside parabolic subgroups of Artin groups; American Mathematical Society; Proceedings of the American Mathematical Society; 151; 4; 4-2023; 1519-1526
0002-9939
CONICET Digital
CONICET
url http://hdl.handle.net/11336/228285
identifier_str_mv Blufstein, Martín Axel; Paris, Luis; Parabolic subgroups inside parabolic subgroups of Artin groups; American Mathematical Society; Proceedings of the American Mathematical Society; 151; 4; 4-2023; 1519-1526
0002-9939
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1090/proc/16289
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2204.05142
info:eu-repo/semantics/altIdentifier/url/https://doi.org/10.48550/arXiv.2204.05142
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 American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
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 13.13397

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