Deformations of 𝔞𝔣𝔣(n|1)-module of weighted densities on ℝ1|n, n ≥ 2

Abstract

Over the [Formula: see text]-dimensional real superspace, [Formula: see text], we study non-trivial deformations of the natural action of the affine Lie superalgebra [Formula: see text] 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 we prove that any formal deformation is equivalent to its infinitesimal part. This work is the simplest generalization of a result by Basdouri and Omri [Cohomology and deformation of [Formula: see text] acting on differential operators, Int. J. Geom. Methods Mod. Phys. 15 (2018) 1850072].