Deformation of modules of weighted densities on the superspace $${\mathbb{R}^{1|N}}$$ R 1 | N

Abstract

Over the (1,N)-dimensional real superspace, $${N \geqq 3}$$ , we study non-trivial deformations of the natural action of the orthosymplectic Lie superalgebra $${\mathfrak{osp}(N|2)}$$ on the direct sum of the superspaces of weighted densities. We compute the necessary and sufficient integrability conditions of a given infinitesimal deformation of this action and prove that any formal deformation is equivalent to its infinitisemal part. Likewise we study the same problem for the Lie superalgebra $${\mathcal{K}(N)}$$ of contact vector fields instead of $${\mathfrak{osp}(N|2)}$$ getting the same results. This work is the simplest generalization of a result by I. Basdouri and M. Ben Ammar [4] and F. Ammar and K. Kammoun [3].