Abstract
Over the (1, n)-dimensional real superspace, we classify aff(n vertical bar 1)-invariant linear differential operators acting on the superspaces of weighted densities, where K(n) is the Lie superalgebra of contact vector fields. This result allows us to compute the first differential cohomology of K(n) with coefficients in the superspace of weighted densities, vanishing on the Lie superalgebra aff(n vertical bar 1). We explicitly give 1-cocycles spanning these cohomology spaces.