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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     author = {N. Ben Fraj and M. Boujelbene},
     title = {Cohomology of $\mathfrak {osp}(2|2)$ {Acting} on {Spaces} of {Linear} {Differential} {Operators} on the {Superspace} $\mathbb{R}^{1|2}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {331--342},
     publisher = {mathdoc},
     volume = {92},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_3_a1/}
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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/