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

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Original languageEnglish
Pages (from-to)86-114
Number of pages29
JournalLinear algebra and its applications
Volume546
Early online date6 Feb 2018
Publication statusPublished - 1 Jun 2018

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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