Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces

Using Bieberbach groups, we study multipermutation involutive solutions to the Yang-Baxter equation. We use a linear representation of the structure group of an involutive solution to study the unique product property in such groups. An algorithm to find subgroups of a Bieberbach group isomorphic to...

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Autores: Acri, Emiliano Francisco, Lutowski, R., Vendramin, Claudio Leandro
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/136766
Acceso en línea:http://hdl.handle.net/11336/136766
Access Level:acceso abierto
Palabra clave:BIEBERBACH GROUP
MULTIPERMUTATION SOLUTION
SET-THEORETIC SOLUTION
SKEW BRACE
UNIQUE PRODUCT PROPERTY
YANG-BAXTER EQUATION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew bracesAcri, Emiliano FranciscoLutowski, R.Vendramin, Claudio LeandroBIEBERBACH GROUPMULTIPERMUTATION SOLUTIONSET-THEORETIC SOLUTIONSKEW BRACEUNIQUE PRODUCT PROPERTYYANG-BAXTER EQUATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Using Bieberbach groups, we study multipermutation involutive solutions to the Yang-Baxter equation. We use a linear representation of the structure group of an involutive solution to study the unique product property in such groups. An algorithm to find subgroups of a Bieberbach group isomorphic to the Promislow subgroup is introduced and then used in the case of structure group of involutive solutions. To extend the results related to retractability to non-involutive solutions, following the ideas of Meng, Ballester-Bolinches and Romero, we develop the theory of right p-nilpotent skew braces. The theory of left p-nilpotent skew braces is also developed and used to give a short proof of a theorem of Smoktunowicz in the context of skew braces.Fil: Acri, Emiliano Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Lutowski, R.. University Of Gdańsk; PoloniaFil: Vendramin, Claudio Leandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaWorld Scientific2019-09info: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/11336/136766Acri, Emiliano Francisco; Lutowski, R.; Vendramin, Claudio Leandro; Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces; World Scientific; International Journal of Algebra and Computation; 30; 1; 9-2019; 91-1150218-1967CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0218196719500656info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218196719500656info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T14:01:55Zoai:ri.conicet.gov.ar:11336/136766instacron: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:34982024-05-08 14:01:55.995CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces
title Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces
spellingShingle Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces
Acri, Emiliano Francisco
BIEBERBACH GROUP
MULTIPERMUTATION SOLUTION
SET-THEORETIC SOLUTION
SKEW BRACE
UNIQUE PRODUCT PROPERTY
YANG-BAXTER EQUATION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces
title_full Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces
title_fullStr Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces
title_full_unstemmed Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces
title_sort Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces
dc.creator.none.fl_str_mv Acri, Emiliano Francisco
Lutowski, R.
Vendramin, Claudio Leandro
author Acri, Emiliano Francisco
author_facet Acri, Emiliano Francisco
Lutowski, R.
Vendramin, Claudio Leandro
author_role author
author2 Lutowski, R.
Vendramin, Claudio Leandro
author2_role author
author
dc.subject.none.fl_str_mv BIEBERBACH GROUP
MULTIPERMUTATION SOLUTION
SET-THEORETIC SOLUTION
SKEW BRACE
UNIQUE PRODUCT PROPERTY
YANG-BAXTER EQUATION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic BIEBERBACH GROUP
MULTIPERMUTATION SOLUTION
SET-THEORETIC SOLUTION
SKEW BRACE
UNIQUE PRODUCT PROPERTY
YANG-BAXTER EQUATION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description Using Bieberbach groups, we study multipermutation involutive solutions to the Yang-Baxter equation. We use a linear representation of the structure group of an involutive solution to study the unique product property in such groups. An algorithm to find subgroups of a Bieberbach group isomorphic to the Promislow subgroup is introduced and then used in the case of structure group of involutive solutions. To extend the results related to retractability to non-involutive solutions, following the ideas of Meng, Ballester-Bolinches and Romero, we develop the theory of right p-nilpotent skew braces. The theory of left p-nilpotent skew braces is also developed and used to give a short proof of a theorem of Smoktunowicz in the context of skew braces.
publishDate 2019
dc.date.none.fl_str_mv 2019-09
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/11336/136766
Acri, Emiliano Francisco; Lutowski, R.; Vendramin, Claudio Leandro; Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces; World Scientific; International Journal of Algebra and Computation; 30; 1; 9-2019; 91-115
0218-1967
CONICET Digital
CONICET
url http://hdl.handle.net/11336/136766
identifier_str_mv Acri, Emiliano Francisco; Lutowski, R.; Vendramin, Claudio Leandro; Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces; World Scientific; International Journal of Algebra and Computation; 30; 1; 9-2019; 91-115
0218-1967
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0218196719500656
info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218196719500656
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 World Scientific
publisher.none.fl_str_mv World Scientific
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15,812429

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