Factorization of the $\mathrm{R}$-matrix. I

We study the general rational solution of the Yang–Baxter equation with the symmetry algebra $s\ell(3)$. The $R$-operator acting in the tensor product of two arbitrary representations of the symmetry algebra can be represented as the product of the simpler “building blocks” – $\mathbb R$-operators. The $\mathbb R$-operators are constructed explicitly and have simple structure. We construct in a such way the general rational solution of the Yang–Baxter equation with the symmetry algebra $s\ell(3)$. To illustrate the factorization in the simplest situation we treat also the $s\ell(2)$ case.