Cohomology of osp(n/2) acting on the spaces of linear differential operators on the superspace R ~(1)

摘要

We compute the first differential cohomology of the orthosym- plectic 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 co- homology. We explicitly give 1-cocycles spanning these cohomology groups. This work is the simplest superization of a result by Lecomte (see: On the cohomol- ogy of sl(n + 1;R) acting on differential operators and sl(n + 1;R)-equivariant symbols, Indag. Math. NS. 11(1), 95{114 (2000).) Mathematics Subject Classification 2010: 53D55, 14F10, 17B10, 17B68.