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Cohomology of \(\mathfrak{osp}(n|2)\) acting on the spaces of linear differential operators on the superspace \(\mathbb R^{1|n}\). (English) Zbl 1346.17011

Summary: We compute the first differential cohomology of the orthosymplectic Lie superalgebra \(\mathfrak {osp}(n|2)\) with coefficients in the superspace of linear differential operators acting on the space of weighted densities on the \((1,n)\)-dimensional real superspace. Likewise we compute its \(\mathfrak{osp}(n-1|2)\)-relative cohomology. We explicitly give 1-cocycles spanning these cohomology groups. This work is the simplest superization of a result by P. B. A. Lecomte [Indag. Math., New Ser. 11, No. 1, 95–114 (2000; Zbl 0990.58017)].

MSC:

17B56 Cohomology of Lie (super)algebras
17B66 Lie algebras of vector fields and related (super) algebras

Citations:

Zbl 0990.58017
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