Singular $$ mathcal{R}$$ -Matrices and Drinfeld's Comultiplication

We compute the $mathcal{R}$ -matrix which intertwines two dimensional evaluation representations with Drinfeld comultiplication for ${text{U}}_q left( {widehat{{text{sl}}}_{text{2}} } right)$ . This $mathcal{R}$ -matrix contains terms proportional to the δ-function. We construct the algebra $Aleft( mathcal{R} right)$ generated by the elements of the matrices L^±(z) with relations determined by $mathcal{R}$ . In the category of highest-weight representations, there is a Hopf algebra isomorphism between $Aleft( mathcal{R} right)$ and an extension $overline {text{U}} _q left( {widehat{{text{sl}}}_{text{2}} } right)$ of Drinfeld's algebra.