# The Binary Invariant Differential Operators on Weighted Densities on the superspace $mathbb{R}^{1|n}$ and Cohomology - Mathematics > Representation Theory

The Binary Invariant Differential Operators on Weighted Densities on the superspace $mathbb{R}^{1|n}$ and Cohomology - Mathematics > Representation Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: Over the $1,n$-dimensional real superspace, $n>1$, we classify$\mathcal{K}n$-invariant binary differential operators acting on thesuperspaces of weighted densities, where $\mathcal{K}n$ is the Liesuperalgebra of contact vector fields. This result allows us to compute thefirst differential cohomology of %the Lie superalgebra $\mathcal{K}n$ withcoefficients in the superspace of linear differential operators acting on thesuperspaces of weighted densities-a superisation of a result by Feigin andFuchs. We explicitly give 1-cocycles spanning these cohomology spaces.

Author: ** Mabrouk Ben Ammar, Nizar Ben Fraj, Salem Omri**

Source: https://arxiv.org/