%0 Journal Article
%T The Binary Invariant Differential Operators on Weighted Densities on the superspace $\mathbb{R}^{1|n}$ and Cohomology
%A Mabrouk Ben Ammar
%A Nizar Ben Fraj
%A Salem Omri
%J Mathematics
%D 2009
%I arXiv
%R 10.1063/1.3355127
%X Over the $(1,n)$-dimensional real superspace, $n>1$, we classify $\mathcal{K}(n)$-invariant binary differential operators acting on the superspaces of weighted densities, where $\mathcal{K}(n)$ is the Lie superalgebra of contact vector fields. This result allows us to compute the first differential cohomology of %the Lie superalgebra $\mathcal{K}(n)$ with coefficients in the superspace of linear differential operators acting on the superspaces of weighted densities--a superisation of a result by Feigin and Fuchs. We explicitly give 1-cocycles spanning these cohomology spaces.
%U http://arxiv.org/abs/0912.5070v1