Geodesic
Cohomology of $\mathfrak {osp}(2|2)$ Acting on Spaces of Linear Differential Operators on the Superspace $\mathbb{R}^{1|2}$
Matematičeskie zametki, Tome 92 (2012) no. 3, pp. 331-342.

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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 cohomologies. This work is the simplest generalization of a result from [1].
Keywords: differential cohomology, orthosymplectic Lie superalgebra, differential operator, superspace, Lie algebra of contact vector fields. 
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N. Ben Fraj; M. Boujelbene. Cohomology of $\mathfrak {osp}(2|2)$ Acting on Spaces of Linear Differential Operators on the Superspace $\mathbb{R}^{1|2}$. Matematičeskie zametki, Tome 92 (2012) no. 3, pp. 331-342. http://geodesic.mathdoc.fr/item/MZM_2012_92_3_a1/

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