Representations of the q-deformed algebras U q(so2,1) and U q(so3,1)

Abstract

Representations of the algebra Uq(so2,1) are studied. This algebra is a q-deformation of the universal enveloping algebra U(so2,1) of the Lie algebra of the group SO0(2,1) and differs from the quantum algebra Uq(su1,1). Classifications of irreducible representations and of infinitesimally unitary irreducible representations of Uq(so2,1), with simple and discrete spectrum of one of generators are derived. The set of infinitesimally unitary representations of Uq(so2,1) does not coincide with that for the algebra Uq(su1,1). The sets of irreducible representations and of infinitesimally unitary irreducible representations of the algebra Uq(so3,1) are given. We also consider representations of Uq(son,1) which are of class 1 with respect to the subalgebra Uq(son).