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).

arXiv comment7 pages

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• On set-theoretical solutions of the quantum Yang-Baxter equation
• Skew braces and the Yang-Baxter equation
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Cited by in corpus (13)

• On structure groups of set-theoretic solutions to the Yang-Baxter equation
• Skew left braces of nilpotent type
• Factorizations of skew braces
• Decomposition theorems for involutive solutions to the Yang-Baxter equation
• Isoclinism of skew braces
• 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