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arXiv · 1704.03558

Set-theoretic solutions of the Yang-Baxter equation and new classes of R-matrices

Agata Smoktunowicz·Alicja Smoktunowicz
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Abstract

We describe several methods of constructing R-matrices that are dependent upon many parameters, for example unitary R-matrices and R-matrices whose entries are functions. As an application, we construct examples of R-matrices with prescribed singular values. We characterise some classes of indecomposable set-theoretic solutions of the quantum Yang-Baxter equation (QYBE) and construct R-matrices related to such solutions. In particular, we establish a correspondence between one-generator braces and indecomposable, non-degenerate involutive set-theoretic solutions of the QYBE, showing that such solutions are abundant. We show that R-matrices related to involutive, non-degenerate solutions of the QYBE have special form. We also investigate some linear algebra questions related to R-matrices.

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Agata Smoktunowicz, Alicja Smoktunowicz. 2017-11-08. Set-theoretic solutions of the Yang-Baxter equation and new classes of R-matrices. https://arxiv.org/abs/1704.03558

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