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(J 0 ) and g(J 0 ) are considered. For g(J 0 )=1, they reduce to some algebras first studied by Polychronakos (1990) and Rocek (1991). Spatial emphasis is laid on the case where g(J 0 ) is a linear function of J 0 . It is shown that for any lambda =2,3,. . ., there exist ( lambda -1)-parameter algebras that are deformations of su(2) or su(1,1) respectively, and for which f(J 0 ) is a polynomial of degree lambda . For lambda =2, such algebras are equivalent to Witten's (1990) first deformation of su(2) or su(1,1). For any lambda , the spectrum of J 0 is exponential instead of linear as in the case where g(J 0 )=1.