Classification of 𝔞𝔣𝔣(3|1)-invariant binary differential operators on weighted densities and cohomology

Abstract

In this paper, we consider the [Formula: see text]-module structure on the spaces of differential bilinear operators acting on the superspaces of weighted densities. We classify [Formula: see text]-invariant binary differential operators acting on the spaces of weighted densities. This result allows us to compute the first [Formula: see text]-relative differential cohomology of [Formula: see text] with coefficients in the superspace of linear differential operators acting on the superspaces of weighted densities. Finally, we deduce the classification of the [Formula: see text]-relative extension of [Formula: see text] modules [Formula: see text]