arXiv subjects

Maha Boujelben

Publications and source records attributed to Maha Boujelben.

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↗

arXiv2011

Cohomology of $\mathfrak {osp}(2|2)$ acting on the spaces of linear differential operators on the superspace $\mathbb{R}^{1|2}$

We compute the first differential cohomology of the orthosymplectic Lie superalgebra $\mathfrak{osp}(2|2)$ with coefficients in the superspace of linear differential operators acting on the space of weighted densities on the (1,\,2)-dimensional real superspace. We also compute the same, but $\mathfrak{osp}(1|2)$-relative, cohomology. We explicitly give 1-cocycles spanning these cohomology. This work is a simplest generalization of a result by Basdouri and Ben Ammar [Cohomology of $\frak {osp}(1|2)$ with coefficients in $\frak{D}_{λ,μ}$.

math.RT↗