
Journal of Lie Theory 23 (2013), No. 2, 575587 Copyright Heldermann Verlag 2013 Cohomology of osp(n2) Acting on the Spaces of Linear Differential Operators on the Superspace R^{1n} Nizar Ben Fraj Institut Préparatoire aux Études d'Ingénieur, Université de Carthage, Campus Universitaire, 8000 Nabeul Merazka, Tunisia benfraj_nizar@yahoo.fr Amina Jabeur Dept. of Mathematics, Faculty of Sciences, University of Sfax, Route de Soukra  B.P.802, 3018 Sfax, Tunisia Imen Safi Dept. of Mathematics, Faculty of Sciences, University of Sfax, Route de Soukra  B.P.802, 3018 Sfax, Tunisia We compute the first differential cohomology of the orthosymplectic Lie superalgebra osp(n2) 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 osp(n12)relative cohomology. We explicitly give 1cocycles spanning these cohomology groups. This work is the simplest superization of a result by Lecomte [see: On the cohomology of sl(n+1,R) acting on differential operators and sl(n+1,R)equivariant symbols, Indag. Math. NS. 111 (2000) 95114]. Keywords: Invariant operators, cohomology, orthosymplectic superalgebra. MSC: 53D55, 14F10, 17B10, 17B68 [ Fulltextpdf (366 KB)] for subscribers only. 