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## Abstract / Description of output

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.

Original language | English |
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Pages (from-to) | 86-114 |

Number of pages | 29 |

Journal | Linear algebra and its applications |

Volume | 546 |

Early online date | 6 Feb 2018 |

Publication status | Published - 1 Jun 2018 |

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