Cohomology of \(\mathfrak {osp}(2|2)\) acting on spaces of linear differential operators on the superspace \(\mathbb{R}^{1|2}\) (Q1929763)

This work gives the computation of the first differential cohomology of \(\mathfrak {osp}(2,2)\) acting on the (1,2)-dimensional real superspace. Let us recall that the computation of the differential cohomology of \(\mathfrak {osp}(n,2)\) is used to classify the deformations of \(\mathfrak {osp}(n,2)\). In this paper, the authors consider the case \(n=2\), that is they consider the orthosymplectic Lie superalgebra \(\mathfrak {osp}(2,2)\). They also give explicit formulas for the nontrivial 1-cocycles. The link with the classification of the infinitesimal deformations of \(\mathfrak {osp}(1,2)\) is made more precise.