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




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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/



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