The representations ofU q(SO4) andU q(SO3,1)

Summary We have considered here the (unitary) irreducible representations of theq-deformed algebraU _q(SO₄) and of theq-deformed Lorentz algebraU _q(SO_3,1). Both of them contain, as subalgebra, the algebraU _q(SO₃) which is shown to be isomorphic to the Fairlie-Odesskii algebra. As the list of pairwise nonequivalent irreps of theU _q(SO_3,1) demonstrates, the set of the parameters, which characterize such irreps is somewhat reduced (due to periodicity properties of the function w(z)=z]_q) in comparison with that of theq=1 (classical) case. From another side, the list of unitary irreps of theU _q(SO_3,1) contains the strange series which has no classical counterpart (disappears at q=1).Published in Teoreticheskaya i Matematicheskaya Fizika. Vol. 95, No. 2, pp. 251–257, May, 1993.