REPRESENTATIONS OF THE GENERALIZED LIE-ALGEBRA SL(2)(Q)

We construct finite-dimensional irreducible representations of two qua ntum algebras related to the generalized Lie algebra sl(2)(q) introduc ed by Lyubashenko and Sudbery. We consider separately the cases of q g eneric and q at roots of unity. Some of the representations have no cl assical 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 mat rix elements.