arXiv subjects

Rabeb Sidaoui

Publications and source records attributed to Rabeb Sidaoui.

2 recordsLinked to original sources

arXiv2018

Cohomology of $\frak {sl}(2)$ acting on the space of $n$-ary differential operators on $\mathbb{R}$

We consider the spaces $\mathcal{F}_μ$ of polynomial $μ$-densities on the line as $\mathfrak{sl}(2)$-modules and then we compute the cohomological spaces $\mathrm{H}^1_\mathrm{diff}(\mathfrak{sl}(2), \mathcal{D}_{\barλ,μ})$, where $μ\in \mathbb{R}$, $\barλ=(λ_1,\dots,λ_n) \in\mathbb{R}^n$ and $\mathcal{D}_{\barλ,μ}$ is the space of $n$-ary differential operators from $\mathcal{F}_{λ_1}\otimes\cdots\otimes \mathcal{F}_{λ_n}$ to $\mathcal{F}_μ$.

math.RT↗

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↗