Abstract:
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.
Registro:
Documento: |
Artículo
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Título: | Yang–Baxter operators in symmetric categories |
Autor: | Guccione, J.A.; Guccione, J.J.; Vendramin, L. |
Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina Instituto de Investigaciones Matemáticas “Luis A. Santaló”, Buenos Aires, Argentina Instituto Argentino de Matemática-CONICET, Buenos Aires, Argentina
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Palabras clave: | Coalgebras; Yang–Baxter equation |
Año: | 2018
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Volumen: | 46
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Número: | 7
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Página de inicio: | 2811
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Página de fin: | 2845
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DOI: |
http://dx.doi.org/10.1080/00927872.2017.1399411 |
Título revista: | Communications in Algebra
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Título revista abreviado: | Commun. Algebra
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ISSN: | 00927872
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00927872_v46_n7_p2811_Guccione |
Referencias:
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Citas:
---------- APA ----------
Guccione, J.A., Guccione, J.J. & Vendramin, L.
(2018)
. Yang–Baxter operators in symmetric categories. Communications in Algebra, 46(7), 2811-2845.
http://dx.doi.org/10.1080/00927872.2017.1399411---------- CHICAGO ----------
Guccione, J.A., Guccione, J.J., Vendramin, L.
"Yang–Baxter operators in symmetric categories"
. Communications in Algebra 46, no. 7
(2018) : 2811-2845.
http://dx.doi.org/10.1080/00927872.2017.1399411---------- MLA ----------
Guccione, J.A., Guccione, J.J., Vendramin, L.
"Yang–Baxter operators in symmetric categories"
. Communications in Algebra, vol. 46, no. 7, 2018, pp. 2811-2845.
http://dx.doi.org/10.1080/00927872.2017.1399411---------- VANCOUVER ----------
Guccione, J.A., Guccione, J.J., Vendramin, L. Yang–Baxter operators in symmetric categories. Commun. Algebra. 2018;46(7):2811-2845.
http://dx.doi.org/10.1080/00927872.2017.1399411