Cohomology of 𝒦(1) acting on the superspace of bilinear differential operators

We consider the [Formula: see text]-dimensional real superspace [Formula: see text] endowed with its standard contact structure defined by the [Formula: see text]-form [Formula: see text]. The conformal Lie superalgebra [Formula: see text] acts on [Formula: see text] as the Lie superalgebra of contact vector fields. We compute the first differential cohomology of [Formula: see text] with coefficients in superspace [Formula: see text] of bilinear differential operators acting on weighted densities. This work is the simplest super analog of the problems solved in Ref. 5.