On the universal $R$-matrix of $U_q\hat{sl}_2$ at roots of unity

Abstract

We show that the action of universal $R$-matrix of affine $U_qsl_2$ quantum algebra, when $q$ is a root of unity, can be renormalized by some scalar factor to give a well defined nonsingular expression, satisfying Yang-Baxter equation. It reduced to intertwining operators of all representations, corresponding to Chiral Potts, if the parameters of these representations lie on well known algebraic curve. We also show that affine $U_qsl_2$ for $q$ is a root of unity form the autoquasitriangular Hopf algebra in the sence of Reshetikhin.