Braces and the Yang–Baxter Equation

@article{Ced2012BracesAT,
  title={Braces and the Yang–Baxter Equation},
  author={Ferran Ced{\'o} and Eric Jespers and Jan Okninski},
  journal={Communications in Mathematical Physics},
  year={2012},
  volume={327},
  pages={101-116}
}
Several aspects of relations between braces and non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation are discussed and many consequences are derived. In particular, for each positive integer n a finite square-free multipermutation solution of the Yang–Baxter equation with multipermutation level n and an abelian involutive Yang–Baxter group is constructed. This answers a problem of Gateva-Ivanova and Cameron. It is proved that finite non-degenerate involutive set… 
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