NONLINEAR DEFORMED SU(2) ALGEBRAS INVOLVING 2 DEFORMING FUNCTIONS

The most common nonlinear deformations of the su(2) Lie algebra, intro duced by Polychronakos and Rocek, involve a single arbitrary function of J(0) and include the quantum algebra su(q)(2) as a special case. In the present contribution, less common nonlinear deformations of su(2) , introduced by Delbecq and Quesne and involving two deforming functio ns of J(0), are reviewed. Such algebras include Witten's quadratic def ormation of su(2) as a special case. Contrary to the former deformatio ns, for which the spectrum of J(0) is linear as for su(2), the latter give rise to exponential spectra, a property that has aroused much int erest in connection with some physical problems. Another interesting a lgebra of this type, denoted by A(q)(+)(1), has two series of (N + 1)- dimensional unitary irreducible representations, where N = 0, 1, 2,... . To allow the coupling of any two such representations, a generalizat ion of the standard Hopf axioms is proposed. The resulting algebraic s tructure, referred to as a two-colour quasitriangular. Hopf algebra, i s described.