ON A DEFORMATION OF SL(2) WITH PARAGRASSMANNIAN VARIABLES

We propose a new structure U-q(r)(sl(2)). This is realized by multiply ing delta(q = e(delta), delta is an element of C) by theta, where thet a is a real nilpotent, paragrassmannian, variable of order r(theta(r+1 ) = 0) that we call the order of deformation, the limit r --> infinity giving back the standard U-q(sl(2)). In particular, we show that for r = 1 there exists a new R-matrix associated with sl(2). We also prove that the restriction of the values of the parameters of deformation g ive nonlinear algebras as particular cases.