On the cohomology of the orthosymplectic superalgebra.

Let $\mathfrak{F}_{\lambda}^{n}$ be the $\mathop {\mathfrak {osp}}\nolimits \,(n|2)$-module of weighted densities on ℝ of weight λ. We compute the cohomology spaces $\mathrm{H}^{k}_{\mathrm{diff}}\left(\mathop {\mathfrak {osp}}\nolimits \,(n|2),\mathfrak{F}_{\lambda}^{n}\right)$, where k=1 and n=0,1,2 or k=2 and n=0,1. We explicitly give cocycles spanning these cohomology spaces. [ABSTRACT FROM AUTHOR]