Involutive Yang–Baxter: cabling, decomposability, and Dehornoy class

Autores
Lebed, Victoria; Ramírez, Santiago Agustín; Vendramin, Leandro
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We develop new machinery for producing decomposability tests for involutive solutions to the Yang–Baxter equation. It is based on the seminal decomposability theorem of Rump and on “cabling” operations on solutions and their effect on the diagonal map T. Our machinery yields an elementary proof of a recent decomposability theorem of Camp-Mora and Sastriques, as well as original decomposability results. It also provides a conceptual interpretation (using the language of braces) of the Dehornoy class, a combinatorial invariant naturally appearing in the Garsidetheoretic approach to involutive solutions.
Fil: Lebed, Victoria. Centre National de la Recherche Scientifique; Francia
Fil: Ramírez, Santiago Agustín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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
Fil: Vendramin, Leandro. Vrije Unviversiteit Brussel; Bélgica
Materia
Yang-Baxter equation
braces
indecomposable solutions
primitive solutions
diagonal map
dehornoy class
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:11336/263662
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Involutive Yang–Baxter: cabling, decomposability, and Dehornoy classLebed, VictoriaRamírez, Santiago AgustínVendramin, LeandroYang-Baxter equationbracesindecomposable solutionsprimitive solutionsdiagonal mapdehornoy classhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We develop new machinery for producing decomposability tests for involutive solutions to the Yang–Baxter equation. It is based on the seminal decomposability theorem of Rump and on “cabling” operations on solutions and their effect on the diagonal map T. Our machinery yields an elementary proof of a recent decomposability theorem of Camp-Mora and Sastriques, as well as original decomposability results. It also provides a conceptual interpretation (using the language of braces) of the Dehornoy class, a combinatorial invariant naturally appearing in the Garsidetheoretic approach to involutive solutions.Fil: Lebed, Victoria. Centre National de la Recherche Scientifique; FranciaFil: Ramírez, Santiago Agustín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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"; ArgentinaFil: Vendramin, Leandro. Vrije Unviversiteit Brussel; BélgicaUniversidad Autónoma de Madrid2023-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/263662Lebed, Victoria; Ramírez, Santiago Agustín; Vendramin, Leandro; Involutive Yang–Baxter: cabling, decomposability, and Dehornoy class; Universidad Autónoma de Madrid; Revista Matematica Iberoamericana; 40; 2; 7-2023; 623-6350213-2230CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://ems.press/doi/10.4171/rmi/1438info:eu-repo/semantics/altIdentifier/doi/10.4171/rmi/1438info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:35:29Zoai:ri.conicet.gov.ar:11336/263662instacron: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 09:35:29.982CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Involutive Yang–Baxter: cabling, decomposability, and Dehornoy class
title Involutive Yang–Baxter: cabling, decomposability, and Dehornoy class
spellingShingle Involutive Yang–Baxter: cabling, decomposability, and Dehornoy class
Lebed, Victoria
Yang-Baxter equation
braces
indecomposable solutions
primitive solutions
diagonal map
dehornoy class
title_short Involutive Yang–Baxter: cabling, decomposability, and Dehornoy class
title_full Involutive Yang–Baxter: cabling, decomposability, and Dehornoy class
title_fullStr Involutive Yang–Baxter: cabling, decomposability, and Dehornoy class
title_full_unstemmed Involutive Yang–Baxter: cabling, decomposability, and Dehornoy class
title_sort Involutive Yang–Baxter: cabling, decomposability, and Dehornoy class
dc.creator.none.fl_str_mv Lebed, Victoria
Ramírez, Santiago Agustín
Vendramin, Leandro
author Lebed, Victoria
author_facet Lebed, Victoria
Ramírez, Santiago Agustín
Vendramin, Leandro
author_role author
author2 Ramírez, Santiago Agustín
Vendramin, Leandro
author2_role author
author
dc.subject.none.fl_str_mv Yang-Baxter equation
braces
indecomposable solutions
primitive solutions
diagonal map
dehornoy class
topic Yang-Baxter equation
braces
indecomposable solutions
primitive solutions
diagonal map
dehornoy class
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 develop new machinery for producing decomposability tests for involutive solutions to the Yang–Baxter equation. It is based on the seminal decomposability theorem of Rump and on “cabling” operations on solutions and their effect on the diagonal map T. Our machinery yields an elementary proof of a recent decomposability theorem of Camp-Mora and Sastriques, as well as original decomposability results. It also provides a conceptual interpretation (using the language of braces) of the Dehornoy class, a combinatorial invariant naturally appearing in the Garsidetheoretic approach to involutive solutions.
Fil: Lebed, Victoria. Centre National de la Recherche Scientifique; Francia
Fil: Ramírez, Santiago Agustín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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
Fil: Vendramin, Leandro. Vrije Unviversiteit Brussel; Bélgica
description We develop new machinery for producing decomposability tests for involutive solutions to the Yang–Baxter equation. It is based on the seminal decomposability theorem of Rump and on “cabling” operations on solutions and their effect on the diagonal map T. Our machinery yields an elementary proof of a recent decomposability theorem of Camp-Mora and Sastriques, as well as original decomposability results. It also provides a conceptual interpretation (using the language of braces) of the Dehornoy class, a combinatorial invariant naturally appearing in the Garsidetheoretic approach to involutive solutions.
publishDate 2023
dc.date.none.fl_str_mv 2023-07
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/11336/263662
Lebed, Victoria; Ramírez, Santiago Agustín; Vendramin, Leandro; Involutive Yang–Baxter: cabling, decomposability, and Dehornoy class; Universidad Autónoma de Madrid; Revista Matematica Iberoamericana; 40; 2; 7-2023; 623-635
0213-2230
CONICET Digital
CONICET
url http://hdl.handle.net/11336/263662
identifier_str_mv Lebed, Victoria; Ramírez, Santiago Agustín; Vendramin, Leandro; Involutive Yang–Baxter: cabling, decomposability, and Dehornoy class; Universidad Autónoma de Madrid; Revista Matematica Iberoamericana; 40; 2; 7-2023; 623-635
0213-2230
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://ems.press/doi/10.4171/rmi/1438
info:eu-repo/semantics/altIdentifier/doi/10.4171/rmi/1438
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 Universidad Autónoma de Madrid
publisher.none.fl_str_mv Universidad Autónoma de Madrid
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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