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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
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
Palabras clave:Coalgebras; Yang–Baxter equation
Año:2018
Volumen:46
Número:7
Página de inicio:2811
Página de fin:2845
DOI: http://dx.doi.org/10.1080/00927872.2017.1399411
Título revista:Communications in Algebra
Título revista abreviado:Commun. Algebra
ISSN:00927872
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00927872_v46_n7_p2811_Guccione

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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