The Binary Invariant Differential Operators on Weighted Densities on the superspace $\mathbb{R}^{1|n}$ and Cohomology

Details The Binary Invariant Differential Operators on Weighted Densities on the superspace $\mathbb{R}^{1|n}$ and Cohomology The Binary Invariant Differential Operators on Weighted Densities on the superspace $\mathbb{R}^{1|n}$ and Cohomology

2009-12-27

arxiv.org/abs/0912.5070v1

JOURNAL OF MATHEMATICAL PHYSICS 51, 043504 (2010)

Mathematics

Representation Theory

Scientific paper

10.1063/1.3355127

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.

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