Representations of the cyclically symmetric q-deformed algebra Uq(so(3))

An algebra homomorphism psi from the nonstandard q-deformed (cyclically sym metric) algebra U-q(so(3)) to the extension (U) over cap(q)(sl(2)) of the H opf algebra U-q(sl(2)) is constructed. Not all irreducible representations (IR) of U-q(sl(2)) can be extended to representations of (U) over cap(q)(sl (2)). Composing the homomorphism psi with irreducible representations of (U ) over cap(q)(sl(2)), we obtain representations of U-q(so(3)). Not all of t hese representations of U-q(so(3)) are irreducible. Reducible representatio ns of U-q(so(3)) are decomposed into irreducible components. In this way we obtain all IR of U-g(so(3)) when q is not a root of unity. A part of these representations turn into IR of the Lie algebra sos when g --> 1.