Cohomology of $\mathfrak {osp}(2|2)$ acting on the spaces of linear differential operators on the superspace $\mathbb{R}^{1|2}$

Details Cohomology of $\mathfrak {osp}(2|2)$ acting on the spaces of linear differential operators on the superspace $\mathbb{R}^{1|2}$ Cohomology of $\mathfrak {osp}(2|2)$ acting on the spaces of linear differential operators on the superspace $\mathbb{R}^{1|2}$

2011-10-31

arxiv.org/abs/1110.6723v1

Mathematics

Representation Theory

Scientific paper

We compute the first differential cohomology of the orthosymplectic Lie superalgebra $\mathfrak{osp}(2|2)$ with coefficients in the superspace of linear differential operators acting on the space of weighted densities on the (1,\,2)-dimensional real superspace. We also compute the same, but $\mathfrak{osp}(1|2)$-relative, cohomology. We explicitly give 1-cocycles spanning these cohomology. This work is a simplest generalization of a result by Basdouri and Ben Ammar [Cohomology of $\frak {osp}(1|2)$ with coefficients in $\frak{D}_{\lambda,\mu}$.

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