Deformation of $\mathfrak{sl}\, (2)$ and $\mathfrak{osp}\, (1|2)$ -modules of symbols

Abstract

We consider the sl(2)-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 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.Mathematics Subject Classification (2010). 17B56, 53D55, 58H15.

osp(1|2)-trivial deformation of osp(2Almoneef, Abdaoui, Ghallabi 2024Heliyon0000View full textAdd to dashboardCite

“…They are proved that the conditions of integrability of the infinitesimal deformation of the second order are necessary and sufficient. In 2012, Basdouri and Ben Ammar [5] classified the deformation of -modules and -modules of symbols. In 2018, Ben Fraj, Abdaoui and Raouafi [11] classified the deformations of -modules of symbols trivial on .…”