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Over the -dimensional real superspace , we classify -invariant bilinear differential operators acting on the superspaces of weighted densities. We compute the second -relative cohomology space of with coefficients in the module of -densities on , where is the Lie superalgebra of contact vector fields on and is the affine Lie superalgebra. This result allows us to compute the second -relative cohomology space of with coefficients in the Poisson superalgebra . We explicitly give 2-cocycles spanning these cohomology spaces. [ABSTRACT FROM AUTHOR]

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