A NOTE ON THE GENERALIZED LIE-ALGEBRA SL(2)(Q)

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