About Hopf braces and crossed products

The present article represents a step forward in the study of the following problem: If A = (A1, A2) and H = (H1, H2) are Hopf braces in a symmetric monoidal category C such that (A1, H1) and (A2, H2) are matched pairs of Hopf algebras, then we want to know under what conditions the pair (A1 ▷◁ H1,...

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Detalhes bibliográficos
Autores: Ramos Pérez, Brais, González Rodríguez, Ramón
Formato: artículo
Fecha de publicación:2025
País:España
Recursos:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:minerva.usc.gal:10347/45209
Acesso em linha:https://hdl.handle.net/10347/45209
Access Level:acceso embargado
Palavra-chave:Symmetric monoidal category
Hopf algebra
Matched pair
Bicrossed product
Smash product
Hopf brace
Drinfeld’s Double
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spelling About Hopf braces and crossed productsRamos Pérez, BraisGonzález Rodríguez, RamónSymmetric monoidal categoryHopf algebraMatched pairBicrossed productSmash productHopf braceDrinfeld’s DoubleThe present article represents a step forward in the study of the following problem: If A = (A1, A2) and H = (H1, H2) are Hopf braces in a symmetric monoidal category C such that (A1, H1) and (A2, H2) are matched pairs of Hopf algebras, then we want to know under what conditions the pair (A1 ▷◁ H1, A2 ▷◁ H2) constitutes a new Hopf brace. We find such conditions for the pairs (A1 ⊗ H1, A2 ▷◁ H2) and (A1 ▷◁ H1, A2♯H2) to be Hopf braces, which are particular situations of the general problem described above, analyzing when these are cocommutative, leading to solutions to the Quantum Yang-Baxter equation. These results are applied to study when the Drinfeld’s Double gives rise to a Hopf brace.SpringerUniversidade de Santiago de Compostela. Departamento de Matemáticas20252025-12-2720252025-12-27journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10347/45209reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostelainstname:Universidad de Santiago de Compostela (USC)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-115155GB-I00 HOMOLOGIA, HOMOTOPIA E INVARIANTES CATEGORICOS EN GRUPOS Y ALGEBRAS NO ASOCIATIVASAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2024-2027 PID2024-155502NB-I0embargoed accesshttp://purl.org/coar/access_right/c_f1cfinfo:eu-repo/semantics/embargoedAccessoai:minerva.usc.gal:10347/452092026-06-15T12:47:27Z
dc.title.none.fl_str_mv About Hopf braces and crossed products
title About Hopf braces and crossed products
spellingShingle About Hopf braces and crossed products
Ramos Pérez, Brais
Symmetric monoidal category
Hopf algebra
Matched pair
Bicrossed product
Smash product
Hopf brace
Drinfeld’s Double
title_short About Hopf braces and crossed products
title_full About Hopf braces and crossed products
title_fullStr About Hopf braces and crossed products
title_full_unstemmed About Hopf braces and crossed products
title_sort About Hopf braces and crossed products
dc.creator.none.fl_str_mv Ramos Pérez, Brais
González Rodríguez, Ramón
author Ramos Pérez, Brais
author_facet Ramos Pérez, Brais
González Rodríguez, Ramón
author_role author
author2 González Rodríguez, Ramón
author2_role author
dc.contributor.none.fl_str_mv Universidade de Santiago de Compostela. Departamento de Matemáticas
dc.subject.none.fl_str_mv Symmetric monoidal category
Hopf algebra
Matched pair
Bicrossed product
Smash product
Hopf brace
Drinfeld’s Double
topic Symmetric monoidal category
Hopf algebra
Matched pair
Bicrossed product
Smash product
Hopf brace
Drinfeld’s Double
description The present article represents a step forward in the study of the following problem: If A = (A1, A2) and H = (H1, H2) are Hopf braces in a symmetric monoidal category C such that (A1, H1) and (A2, H2) are matched pairs of Hopf algebras, then we want to know under what conditions the pair (A1 ▷◁ H1, A2 ▷◁ H2) constitutes a new Hopf brace. We find such conditions for the pairs (A1 ⊗ H1, A2 ▷◁ H2) and (A1 ▷◁ H1, A2♯H2) to be Hopf braces, which are particular situations of the general problem described above, analyzing when these are cocommutative, leading to solutions to the Quantum Yang-Baxter equation. These results are applied to study when the Drinfeld’s Double gives rise to a Hopf brace.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-12-27
2025
2025-12-27
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10347/45209
url https://hdl.handle.net/10347/45209
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-115155GB-I00 HOMOLOGIA, HOMOTOPIA E INVARIANTES CATEGORICOS EN GRUPOS Y ALGEBRAS NO ASOCIATIVAS
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2024-2027 PID2024-155502NB-I0
dc.rights.none.fl_str_mv embargoed access
http://purl.org/coar/access_right/c_f1cf
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/embargoedAccess
rights_invalid_str_mv embargoed access
http://purl.org/coar/access_right/c_f1cf
eu_rights_str_mv embargoedAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
instname:Universidad de Santiago de Compostela (USC)
instname_str Universidad de Santiago de Compostela (USC)
reponame_str Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
collection Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
repository.name.fl_str_mv
repository.mail.fl_str_mv
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