Factorization of the R-matrix and Baxter's Q-operator

The general rational solution of the Yang–Baxter equation with the symmetry algebra $s\ell(2)$ can be represented as the product of the simpler building blocks denoted as $\mathcal R$-operators. The $\mathcal R$-operators are constructed explicitly and have simple structure. Using the $\mathcal R$-operators we construct the two-parametric Baxter's Q-operator for the generic inhomogeneous XXX-spin chain. In the case of homogeneous XXX-spin chain it is possible to reduce the general Q-operator to the much simpler one-parametric Q-operator.