  We construct finite-dimensional irreducible representations of two quantum
algebras related to the generalized Lie algebra $\ssll (2)_q$ 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.
