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A characterization of finite multipermutation solutions of the Yang-Baxter equation. (English) Zbl 1432.16030

Summary: 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-\(\mathbb{Z}\).

MSC:

16T25 Yang-Baxter equations
20F16 Solvable groups, supersolvable groups
20F60 Ordered groups (group-theoretic aspects)
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