Yang-Baxter operators in symmetric categories
Quantum Algebra
2018-04-04 v3 Rings and Algebras
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.
Cite
@article{arxiv.1610.05999,
title = {Yang-Baxter operators in symmetric categories},
author = {J. A. Guccione and J. J. Guccione and L. Vendramin},
journal= {arXiv preprint arXiv:1610.05999},
year = {2018}
}
Comments
35 pages, several figures. Final version