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arXiv · 1610.05999

Yang-Baxter operators in symmetric categories

J. A. Guccione·J. J. Guccione·L. Vendramin
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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.

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J. A. Guccione, J. J. Guccione, L. Vendramin. 2017-10-10. Yang-Baxter operators in symmetric categories. https://doi.org/10.1080/00927872.2017.1399411

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