Representations of the cyclically symmetric q-deformed algebra U q(so3)

An algebra homomorphism from the nonstandard q-deformed (cyclically symmetric) algebra U_q(so₃) to the extension Û_q(sl₂) of the Hopf algebra U_q(sl₂) is constructed. Not all irreducible representations (IR) of U_q(sl₂) can be extended to representations of Û_q(sl₂). Composing the homomorphism with irreducible representations of Û_q(sl₂) we obtain representations of U_q(so₃). Not all of these representations of U_q(so₃) are irreducible. Reducible representations of U_q(so₃) are decomposed into irreducible components. In this way we obtain all IR of U_q(so₃) when q is not a root of unity. A part of these representations turn into IR of the Lie algebra so₃ when q 1.