arXiv subjects
Publications and source records attributed to Imen Safi.
Let $\frak F_ł$ be the space of tensor densities of degree $λ$ on the supercircle $S^{1|1}$. We consider the space $\mathfrak{D}_{λ,μ}^k$ of k-th order linear differential operators from $\frak F_ł$ to $\frak F_μ$ as $\mathfrak{osp}(1|2)$-module and we determine the space $\mathfrak{I}_{λ,μ}^k$ of linear maps on $\mathfrak{D}_{λ,μ}^k$ commuting with the $\mathfrak{osp}(1|2)$-action.
We compute the first cohomology of the ortosymplectic Lie superalgebra $\mathfrak{osp}(1|2)$ on the (1,1)-dimensional real superspace with coefficients in the superspace $\frak{D}_{λ,ν;μ}$ of bilinear differential operators acting on weighted densities. This work is the simplest superization of a result by Bouarroudj [Cohomology of the vector fields Lie algebras on $\mathbb{R}\mathbb{P}^1$ acting on bilinear differential operators, International Journal of Geometric Methods in Modern Physics (2005), {\bf 2}; N 1, 23-40].