Ben Fraj, Nizar; Jabeur, Amina; Safi, Imen 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 J. Lie Theory 23, No. 2, 575-587 (2013). 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)]. Cited in 1 Document MSC: 17B56 Cohomology of Lie (super)algebras 17B66 Lie algebras of vector fields and related (super) algebras Keywords:invariant operators; cohomology; orthosymplectic superalgebra Citations:Zbl 0990.58017 PDFBibTeX XMLCite \textit{N. Ben Fraj} et al., J. Lie Theory 23, No. 2, 575--587 (2013; Zbl 1346.17011) Full Text: Link