$\mathfrak{osp}(1|2)$-cohomology on multidifferential operators space

Abstract

We compute cohomology spaces of the ortosymplectic Lie superalgebra $\mathfrak{osp}(1|2)$ on the (1,1)-dimensional real superspace with coefficients in the superspace $\frak{D}_{λ,μ}$ of $n$-ary differential operators acting on weighted densities ($λ\in\mathbb{R}^n$ and $μ\in\mathbb{R}$).