Quasitriangular pointed Hopf algebras
by
Adriana Nenciu
Institute of Mathematics of the Romanian Academy

We study the quasitriangular structures for a family of pointed Hopf algebras introduced by Beattie, Dascalescu and Grunenfelder as examples of pointed Hopf algebras and constructed by Ore extensions with zero derivations. We define the Hopf algebra denoted by H(m, n, d, u) by generators and relations and we give necessary and sufficient conditions for H(m, n, d, u) to be quasitriangular. As a consequence we obtain that if H(m, n, d, u) is quasitriangular then n_j=2 for all j=1, ..., t and in this case we determine completely all the quasitriangular structures of H(m, 2, d, u). Also we determine the ribbon elements of H(m, 2, d, u) and the quasi-ribbon elements of D(H(m, 2, d, u)), the Drinfel'd double of H(m, 2, d, u).

Date received: August 7, 2000

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