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 Sudbery. We consider separately the cases of q generic and q at roots of unity. Some of the representations have no classical analogue even for generic q. Some of the representations have no analogue to the finite-dimensional representations of the quantized enveloping U-q(sl(2)), while in those that do there are different matrix elements.