### Abstract

© 2016 Elsevier Inc. Given a left brace B, a method is given to construct explicitly all the non-degenerate involutive set-theoretic solutions (X,r) of the Yang–Baxter equation such that the associated permutation group G(X,r) is isomorphic, as a left brace, to B. This method depends entirely on the brace structure of B.

Original language | English |
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Pages (from-to) | 80-102 |

Journal | Journal of Algebra |

Volume | 463 |

DOIs | |

Publication status | Published - 1 Oct 2016 |

### Keywords

- Brace
- Set-theoretic solution
- Yang–Baxter equation

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## Cite this

Bachiller, D., Cedó, F., & Jespers, E. (2016). Solutions of the Yang–Baxter equation associated with a left brace.

*Journal of Algebra*,*463*, 80-102. https://doi.org/10.1016/j.jalgebra.2016.05.024