Abstract
We prove that a finite non-degenerate involutive set-theoretic solution $(X,r)$ of the Yang–Baxter equation is a multipermutation solution if and only if its structure group $G(X,r)$ admits a left ordering or equivalently it is poly-$\mathbb{Z}$.
Citation
D. Bachiller. F. Cedó. L. Vendramin. "A characterization of finite multipermutation solutions of the Yang–Baxter equation." Publ. Mat. 62 (2) 641 - 649, 2018. https://doi.org/10.5565/PUBLMAT6221809
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