Factorization of the <Emphasis Type="Italic">R</Emphasis>-matrix. I

We study the general rational solution of the Yang-Baxter equation with the symmetry algebra sℓ(3). The R-operator which acts in the tensor product of two arbitrary representations of the symmetry algebra can be represented as a product of simpler “building blocks,” R-operators. The R-operators are constructed explicitly and have a simple structure. In such a way, we construct the general rational solution of the Yang-Baxter equation with the symmetry algebra s sℓ(3). To illustrate the factorization in the simplest situation, we treat also the sℓ(2) case. Bibliography: 23 titles. Published in Zapiski Nauchnykh Seminarov POMI, Vol. 335, 2006, pp. 134–163.