Yang–Baxter operators in symmetric categories

We introduce non-degenerate solutions of the Yang–Baxter equation in the setting of symmetric monoidal categories. Our theory includes non-degenerate set-theoretical solutions as basic examples. However, infinite families of non-degenerate solutions (that are not of set-theoretical type) appear. As...

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Detalles Bibliográficos
Autores principales: Guccione, J.A., Guccione, J.J., Vendramin, L.
Formato: JOUR
Materias:
Coalgebras
Yang–Baxter equation
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00927872_v46_n7_p2811_Guccione
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00927872_v46_n7_p2811_Guccione
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spelling todo:paper_00927872_v46_n7_p2811_Guccione2023-10-03T14:55:17Z Yang–Baxter operators in symmetric categories Guccione, J.A. Guccione, J.J. Vendramin, L. Coalgebras Yang–Baxter equation We introduce non-degenerate solutions of the Yang–Baxter equation in the setting of symmetric monoidal categories. Our theory includes non-degenerate set-theoretical solutions as basic examples. However, infinite families of non-degenerate solutions (that are not of set-theoretical type) appear. As in the classical theory of Etingof, Schedler, and Soloviev, non-degenerate solutions are classified in terms of invertible 1-cocycles. Braces and matched pairs of cocommutative Hopf algebras (or braiding operators) are also generalized to the context of symmetric monoidal categories and turn out to be equivalent to invertible 1-cocycles. © 2017 Taylor & Francis. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00927872_v46_n7_p2811_Guccione
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Coalgebras
Yang–Baxter equation
spellingShingle Coalgebras
Yang–Baxter equation
Guccione, J.A.
Guccione, J.J.
Vendramin, L.
Yang–Baxter operators in symmetric categories
topic_facet Coalgebras
Yang–Baxter equation
description We introduce non-degenerate solutions of the Yang–Baxter equation in the setting of symmetric monoidal categories. Our theory includes non-degenerate set-theoretical solutions as basic examples. However, infinite families of non-degenerate solutions (that are not of set-theoretical type) appear. As in the classical theory of Etingof, Schedler, and Soloviev, non-degenerate solutions are classified in terms of invertible 1-cocycles. Braces and matched pairs of cocommutative Hopf algebras (or braiding operators) are also generalized to the context of symmetric monoidal categories and turn out to be equivalent to invertible 1-cocycles. © 2017 Taylor & Francis.
format JOUR
author Guccione, J.A.
Guccione, J.J.
Vendramin, L.
author_facet Guccione, J.A.
Guccione, J.J.
Vendramin, L.
author_sort Guccione, J.A.
title Yang–Baxter operators in symmetric categories
title_short Yang–Baxter operators in symmetric categories
title_full Yang–Baxter operators in symmetric categories
title_fullStr Yang–Baxter operators in symmetric categories
title_full_unstemmed Yang–Baxter operators in symmetric categories
title_sort yang–baxter operators in symmetric categories
url http://hdl.handle.net/20.500.12110/paper_00927872_v46_n7_p2811_Guccione
work_keys_str_mv AT guccioneja yangbaxteroperatorsinsymmetriccategories
AT guccionejj yangbaxteroperatorsinsymmetriccategories
AT vendraminl yangbaxteroperatorsinsymmetriccategories
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