2 0 M ar 1 99 8 Representations of the Generalized Lie Algebra sl ( 2 ) q

We construct finite-dimensional irreducible representations of two quantum algebras related to the generalized Lie algebra sl(2) q introduced by Lyubashenko and the second named author. We consider separately the cases of q generic and q at roots of unity. Some of the representations have no classical analog even for generic q. Some of the representations have no analog to the finite-dimensional representations of the quantised enveloping algebra U q (sl(2)), while in those that do there are different matrix elements.