Quasitriangularity of quantum groups at roots of 1

Abstract

An important property of a Hopf algebra is its quasitriangularity and it is useful various applications. This property is investigated for quantum groups $s{l}_2$ at roots of 1. It is shown that different forms of the quantum group $s{l}_2$ at roots of 1 are either quasitriangular or have similar structure which will be called autoquasitriangularity. In the most interesting cases this property means that "braiding automorphism" is a combination of some Poisson transformation and an adjoint transformation with certain element of the tensor square of the algebra.

23 pages

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