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

Abstract

An algebra homomorphism ψ from the nonstandard q-deformed (cyclically symmetric) algebra Uq(so3) to the extension Uq(sl2) of the Hopf algebra Uq(sl2) is constructed. Not all irreducible representations (IR) of Uq(sl2) can be extended to representations of Uq(sl2). Composing the homomorphism ψ with irreducible representations of Uq(sl2) we obtain representations of Uq(so3). Not all of these representations of Uq(so3) are irreducible. Reducible representations of Uq(so3) are decomposed into irreducible components. In this way we obtain all IR of Uq(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.