Symmetric group

Automorphism

Combinatorics

Physics

Pure mathematics

Permutation (music)

Mathematics

Abelian group

Acoustics

Quantum mechanics

Algebra over a field

Cyclic permutation

Group (periodic table)

Discrete mathematics

Indecomposable module

Permutation group

Forum Mathematicum

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.

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