Nonlinear deformations of su(2) and su(1,1). Generalizing witten's algebra

Nonlinear deformations of su(2) and su(1,1) involving two deforming functions f(J0) and J(0) is a linear function of J0, for any lambda=2,3,..., there exist (lambda-1)-parameter algebras A+- - alpha2 alpha3...alpha lambda-1q(alpha,1) for which f(J0) is a lambda th-degree polynomial. For lambda=2, they are equivalent to Witten's first deformations of su(2)or su(1,1). The spectrum of J0 is exponential instead of linear as in the case where g(J0)=1. The representation theory A+- - alpha2 alpha3...alpha lambda-1q(lambda,1) is outlined and the unitary irreducible representations of A+- q (2,1) are listed. (Author) 13 refs