A characterization of finite multipermutation solutions of the Yang-Baxter equation

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-(infinite cyclic).

7 pages

References in corpus (1)

• Retractability of set theoretic solutions of the Yang-Baxter equation

Cited by in corpus (13)

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• Combinatorial solutions to the reflection equation
• Retractability of solutions to the Yang-Baxter equation and $p$-nilpotency of skew braces
• Skew braces: a brief survey
• Set-theoretic solutions of the Yang--Baxter equation, associated quadratic algebras and the minimality condition
• New Solutions to the Reflection Equation with Braces
• Towards semi-trusses
• Hopf brace, braid equation and bicrossed coproduct
• Quasi-bialgebras from set-theoretic type solutions of the Yang-Baxter equation