Factorization of the Universal R-matrix for U_q(hat{sl}₂)

The factorization of the universal R-matrix corresponding to so called Drinfeld Hopf structure is described on the example of quantum affine algebra $U_q(\hat{sl}_2)$. As a result of factorization procedure we deduce certain differential equations on the factors of the universal ${\cal R}$-matrix, which allow to construct uniquely these factors in the integral form.