We consider the -module structure on the spaces of symbols of differential operators acting on the spaces of weighted densities. We compute the necessary and sufficient integrability conditions of a given infinitesimal deformation of this structure and prove that any formal deformation is equivalent to its infinitesimal part. We study also the super analogue of this problem getting the same results.
Authors:Nader Belghith, Mabrouk Ben Ammar, and Nizar Ben Fraj
Over the (1, 1)-dimensional real supercircle, we consider the K(1)-modules Dλ,μk of linear differential operators of order k acting on the superspaces of weighted densities, where K(1) is the Lie superalgebra of contact vector fields. We give, in contrast to the classical setting, a classification of these modules. This work is the simplest superization of a result by Gargoubi and Ovsienko.