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29 March 2024
 
  » arxiv » 1610.5999

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Yang-Baxter operators in symmetric categories
J. A. Guccione ; J. J. Guccione ; L. Vendramin ;
Date 19 Oct 2016
AbstractWe 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.
Source arXiv, 1610.5999
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