  In a recent paper, V. Dobrev and A. Sudbery classified the highest-weight and
lowest-weight finite dimensional irreducible representations of the quantum Lie
algebra sl(2)_q introduced by V. Lyubashenko and A. Sudbery. The aim of this
note is to add to this classification all the finite dimensional irreducible
representations which have no highest weight and/or no lowest weight, in the
case when q is a root of unity. For this purpose, we give a description of the
enlarged centre.
