Deformation of sl(2) and osp(1|2)-Modules of Symbols

Abstract

We consider the sl(2)-module structure on the spaces of symbols of differential opera- tors acting on the spaces of weighted densities. We compute the necessary and sufficient integrability conditions of a given infinitesimal deformation of this structure and we prove that any formal deformation is equivalent to its infinitesimal part. We study also the super analogue of this problem getting the same results.