ON AUTOMORPHISMS AND UNIVERSAL R-MATRICES AT ROOTS OF UNITY

Invertible universal R-matrices of quantum Lie algebras do not exist a t roots of unity. However, quotients exist for which intertwiners of t ensor products of representations always exist, i.e. R-matrices exist in the representations. One of these quotients, which is finite-dimens ional, has a universal R-matrix. In this Letter we answer the followin g question: under which condition are the different quotients of U(q)( sl(2)) (Hopf)-equivalent? In the case when they are equivalent, the un iversal R-matrix of the one can be transformed into a universal R-matr ix of the other. We prove that this happens only when q4 = 1, and we e xplicitly give the expressions for the automorphisms and for the trans formed universal R-matrices in this case.