### Abstract

© 2018 American Mathematical Society. Braces were introduced by Rump as a promising tool in the study of the set-theoretic solutions of the Yang-Baxter equation. It has been recently proved that, given a left brace B, one can construct explicitly all the non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation such that the associated permutation group is isomorphic, as a left brace, to B. It is hence of fundamental importance to describe all simple objects in the class of finite left braces. In this paper we focus on the matched product decompositions of an arbitrary finite left brace. This is used to construct new families of finite simple left braces.

Original language | English |
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Pages (from-to) | 4881-4907 |

Journal | Transactions of the American Mathematical Society |

Volume | 370 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1 Jul 2018 |

### Keywords

- Brace
- Matched product
- Set-theoretic solution
- Simple
- Yang-Baxter equation

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## Cite this

Bachiller, D., Cedó, F., Jespers, E., & Okniński, J. (2018). Iterated matched products of finite braces and simplicity; new solutions of the yang-baxter equation.

*Transactions of the American Mathematical Society*,*370*(7), 4881-4907. https://doi.org/10.1090/tran/7180