The Yang-Baxter equation and Thompson's group $F$

Abstract

In analogy with non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation and braces, we define non-degenerate involutive partial set-theoretic solutions and partial braces. We define the structure group and the structure inverse monoid of such a solution and prove that if the partial solution is square-free, then its structure inverse monoid embeds into the restricted product of a commutative inverse monoid and an inverse symmetric monoid. Furthermore, we show that there exists a square-free, non-degenerate involutive partial solution with structure group isomorphic to Thompson's group $F$.

arXiv commentmany figures- added some changes and a correction to theorem 2, changes in its proof also. margin comments are added to point the changes from the previous version

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Cited by in corpus (1)

• Structure groupoids of quiver-theoretic Yang-Baxter maps