Factorizations of skew braces

Autores
Jespers, E.; Kubat, L.; Van Antwerpen, A.; Vendramin, Claudio Leandro
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We introduce strong left ideals of skew braces and prove that they produce non-trivial decomposition of set-theoretic solutions of the Yang–Baxter equation. We study factorization of skew left braces through strong left ideals and we prove analogs of Itô’s theorem in the context of skew left braces. As a corollary, we obtain applications to the retractability problem of involutive non-degenerate solutions of the Yang–Baxter equation. Finally, we classify skew braces that contain no non-trivial proper characteristic ideals.
Fil: Jespers, E.. Vrije Unviversiteit Brussel; Bélgica
Fil: Kubat, L.. Vrije Unviversiteit Brussel; Bélgica
Fil: Van Antwerpen, A.. Vrije Unviversiteit Brussel; Bélgica
Fil: Vendramin, Claudio Leandro. Institute of Mathematical Sciences at NYU Shanghai; China. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
FACTORIZATION
YANG-BAXTER
BRACE
RADICAL RING
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:11336/136170
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/136170
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Factorizations of skew bracesJespers, E.Kubat, L.Van Antwerpen, A.Vendramin, Claudio LeandroFACTORIZATIONYANG-BAXTERBRACERADICAL RINGhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We introduce strong left ideals of skew braces and prove that they produce non-trivial decomposition of set-theoretic solutions of the Yang–Baxter equation. We study factorization of skew left braces through strong left ideals and we prove analogs of Itô’s theorem in the context of skew left braces. As a corollary, we obtain applications to the retractability problem of involutive non-degenerate solutions of the Yang–Baxter equation. Finally, we classify skew braces that contain no non-trivial proper characteristic ideals.Fil: Jespers, E.. Vrije Unviversiteit Brussel; BélgicaFil: Kubat, L.. Vrije Unviversiteit Brussel; BélgicaFil: Van Antwerpen, A.. Vrije Unviversiteit Brussel; BélgicaFil: Vendramin, Claudio Leandro. Institute of Mathematical Sciences at NYU Shanghai; China. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaSpringer2019-09-20info: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/11336/136170Jespers, E.; Kubat, L.; Van Antwerpen, A.; Vendramin, Claudio Leandro; Factorizations of skew braces; Springer; Mathematische Annalen; 375; 3-4; 20-9-2019; 1649-16630025-5831CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00208-019-01909-1info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00208-019-01909-1info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1905.05886info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:35:41Zoai:ri.conicet.gov.ar:11336/136170instacron: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:34982025-09-29 09:35:41.547CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Factorizations of skew braces
title Factorizations of skew braces
spellingShingle Factorizations of skew braces
Jespers, E.
FACTORIZATION
YANG-BAXTER
BRACE
RADICAL RING
title_short Factorizations of skew braces
title_full Factorizations of skew braces
title_fullStr Factorizations of skew braces
title_full_unstemmed Factorizations of skew braces
title_sort Factorizations of skew braces
dc.creator.none.fl_str_mv Jespers, E.
Kubat, L.
Van Antwerpen, A.
Vendramin, Claudio Leandro
author Jespers, E.
author_facet Jespers, E.
Kubat, L.
Van Antwerpen, A.
Vendramin, Claudio Leandro
author_role author
author2 Kubat, L.
Van Antwerpen, A.
Vendramin, Claudio Leandro
author2_role author
author
author
dc.subject.none.fl_str_mv FACTORIZATION
YANG-BAXTER
BRACE
RADICAL RING
topic FACTORIZATION
YANG-BAXTER
BRACE
RADICAL RING
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 introduce strong left ideals of skew braces and prove that they produce non-trivial decomposition of set-theoretic solutions of the Yang–Baxter equation. We study factorization of skew left braces through strong left ideals and we prove analogs of Itô’s theorem in the context of skew left braces. As a corollary, we obtain applications to the retractability problem of involutive non-degenerate solutions of the Yang–Baxter equation. Finally, we classify skew braces that contain no non-trivial proper characteristic ideals.
Fil: Jespers, E.. Vrije Unviversiteit Brussel; Bélgica
Fil: Kubat, L.. Vrije Unviversiteit Brussel; Bélgica
Fil: Van Antwerpen, A.. Vrije Unviversiteit Brussel; Bélgica
Fil: Vendramin, Claudio Leandro. Institute of Mathematical Sciences at NYU Shanghai; China. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We introduce strong left ideals of skew braces and prove that they produce non-trivial decomposition of set-theoretic solutions of the Yang–Baxter equation. We study factorization of skew left braces through strong left ideals and we prove analogs of Itô’s theorem in the context of skew left braces. As a corollary, we obtain applications to the retractability problem of involutive non-degenerate solutions of the Yang–Baxter equation. Finally, we classify skew braces that contain no non-trivial proper characteristic ideals.
publishDate 2019
dc.date.none.fl_str_mv 2019-09-20
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/11336/136170
Jespers, E.; Kubat, L.; Van Antwerpen, A.; Vendramin, Claudio Leandro; Factorizations of skew braces; Springer; Mathematische Annalen; 375; 3-4; 20-9-2019; 1649-1663
0025-5831
CONICET Digital
CONICET
url http://hdl.handle.net/11336/136170
identifier_str_mv Jespers, E.; Kubat, L.; Van Antwerpen, A.; Vendramin, Claudio Leandro; Factorizations of skew braces; Springer; Mathematische Annalen; 375; 3-4; 20-9-2019; 1649-1663
0025-5831
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/s00208-019-01909-1
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00208-019-01909-1
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1905.05886
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 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 13.070432

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