On the indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level

In this paper, we study the class of indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level, recently introduced by Cedó and Okninski in [13]. We give a group-theoretic characterization of these solutions by means of displacement groups, and we apply this result to...

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Detalles Bibliográficos
Autor: Castelli, Marco
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:318138
Acceso en línea:https://ddd.uab.cat/record/318138
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6922509
Access Level:acceso abierto
Palabra clave:Imprimitive group
Yang-Baxter equation
Brace
Cycle set
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spelling On the indecomposable involutive solutions of the Yang-Baxter equation of finite primitive levelCastelli, MarcoImprimitive groupYang-Baxter equationBraceCycle setIn this paper, we study the class of indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level, recently introduced by Cedó and Okninski in [13]. We give a group-theoretic characterization of these solutions by means of displacement groups, and we apply this result to compute and enumerate those having small size. For some classes of indecomposable involutive solutions recently studied in the literature, we compute the exact value of the primitive level. Some relationships with other families of solutions are also discussed. Finally, following [13, Question 3.2], we provide a complete description of those having primitive level 2 by left braces. 22025-01-0120252025-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/318138https://dx.doi.org/urn:doi:10.5565/PUBLMAT6922509reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:3181382026-06-06T12:50:31Z
dc.title.none.fl_str_mv On the indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level
title On the indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level
spellingShingle On the indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level
Castelli, Marco
Imprimitive group
Yang-Baxter equation
Brace
Cycle set
title_short On the indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level
title_full On the indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level
title_fullStr On the indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level
title_full_unstemmed On the indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level
title_sort On the indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level
dc.creator.none.fl_str_mv Castelli, Marco
author Castelli, Marco
author_facet Castelli, Marco
author_role author
dc.subject.none.fl_str_mv Imprimitive group
Yang-Baxter equation
Brace
Cycle set
topic Imprimitive group
Yang-Baxter equation
Brace
Cycle set
description In this paper, we study the class of indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level, recently introduced by Cedó and Okninski in [13]. We give a group-theoretic characterization of these solutions by means of displacement groups, and we apply this result to compute and enumerate those having small size. For some classes of indecomposable involutive solutions recently studied in the literature, we compute the exact value of the primitive level. Some relationships with other families of solutions are also discussed. Finally, following [13, Question 3.2], we provide a complete description of those having primitive level 2 by left braces.
publishDate 2025
dc.date.none.fl_str_mv 2
2025-01-01
2025
2025-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/318138
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6922509
url https://ddd.uab.cat/record/318138
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6922509
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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