Indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level 2 with abelian permutation group

Abstract

We present a construction of all finite indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level at most 2 with abelian permutation group. As a consequence, we obtain a formula for the number of such solutions with a fixed number of elements. We also describe some properties of the automorphism groups in this case - in particular, we show they are regular abelian groups.