arXiv subjects

Amina Jabeur

Publications and source records attributed to Amina Jabeur.

2 recordsLinked to original sources

arXiv2016

Cohomology of $\mathfrak {aff}(1)$ and $\mathfrak {aff}(1|1)$ acting on the space of $n$-ary differential operators on the superspace $\mathbb{R}^{1|1}$

We consider the $μ$-densities spaces $\mathcal{F}_μ$ with $μ\in\mathbb{R}$, we compute the space $\mathrm{H}^1_\mathrm{diff}(\mathfrak{aff}(1),\mathrm{D}_{λ,μ})$ where $λ=(λ_1,\dots,λ_n)\in\mathbb{R}^n$ and $\mathrm{D}_{λ,μ}$ is the space of $n$-ary differential operators from $\mathcal{F}_{λ_1}\otimes\cdots\otimes\mathcal{F}_{λ_n}$ to $\mathcal{F}_μ$. We also compute the super analog space $\mathrm{H}^1_\mathrm{diff}(\mathfrak{aff}(1|1),\mathfrak{D}_{λ,μ})$.

math.RT↗

arXiv2009

Cohomology of $\frak {osp}(1|2)$ acting on the space of bilinear differential operators on the superspace $\mathbb{R}^{1|1}$

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].

math.RT↗