Journal of Lie Theory 23 (2013), No. 2, 575--587
Copyright Heldermann Verlag 2013
Cohomology of osp(n|2) Acting on the Spaces of Linear Differential Operators on the Superspace R1|n
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(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 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 Lecomte [see: On the cohomology of sl(n+1,R) acting on differential operators and sl(n+1,R)-equivariant symbols, Indag. Math. NS. 11-1 (2000) 95--114].
Keywords: Invariant operators, cohomology, orthosymplectic superalgebra.
MSC: 53D55, 14F10, 17B10, 17B68
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