Extensions of set-theoretic solutions of the Yang-Baxter equation and a conjecture of Gateva-Ivanova

Abstract

We develop a theory of extensions for involutive and nondegenerate solutions of the set-theoretic Yang-Baxter equation and use it to produce new families of solutions. As an application we construct an infinite family of counterexamples to a conjecture of Gateva-Ivanova related to the retractability of square-free solutions.

12 pages

References in corpus (1)

• Semigroups of I-type

Cited by in corpus (21)

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• Iterated matched products of finite braces and simplicity; new solutions of the Yang-Baxter equation
• Left non-degenerate set-theoretic solutions of the Yang-Baxter equation and dynamical extensions of q-cycle sets
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