Multipermutation solutions of the Yang--Baxter equation

Abstract

Set-theoretic solutions of the Yang--Baxter equation form a meeting-ground of mathematical physics, algebra and combinatorics. Such a solution consists of a set $X$ and a function r:X x X --> X x X which satisfies the braid relation. We examine solutions here mainly from the point of view of finite permutation groups: a solution gives rise to a map from $X$ to the symmetric group $Sym(X)$ on $X$ satisfying certain conditions. Our results include many new constructions based on strong twisted union and wreath product, with an investigation of retracts and the multipermutation level and the solvable length of the groups defined by the solutions and new results about decompositions and factorisations of the groups defined by invariant subsets of the solution.

References in corpus (4)

• Yang-Baxter maps: dynamical point of view
• Retractability of set theoretic solutions of the Yang-Baxter equation
• Quantum spaces associated to multipermutation solutions of level two
• Involutive Yang-Baxter Groups

Cited by in corpus (1)

• Garside structure on monoids with quadratic square-free relations