Affine nontrivial Deformation of sl(2) and osp(1/2)-Modules of

Abstract

WE consider  the sl(2)-module structure on the spaces of symbols of diierential operators acting on the spaces of weighted densities. We compute the necessary and sufficient integrability conditions of a given a(1)nonrelative infinitesimal deformation of this structure and prove that any a(1)nonrelative formal deformation is equivalent to its infinitesimal part. We study also the super analogue of this problem getting the same results. This work is the simplest generalization nonrelative  of resalt by Imed Basdouri et al., in ACA MATH HUNGARICA. vol137, Issue 3, 2012.