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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.09199 |
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| _version_ | 1866916134966525952 |
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| author | Ammar, Mabrouk Ben |
| author_facet | Ammar, Mabrouk Ben |
| contents | 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 $\mathrm{H}^2_\mathrm{diff}(\mathfrak{sl}(2), \mathcal{D}_{\barλ,μ})$, 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 $\mathcal{F}_μ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09199 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Second cohomology space of $\frak {sl}(2)$ acting on the space of $n$-ary differential operators on $\mathbb{R}$ Ammar, Mabrouk Ben Differential Geometry 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 $\mathrm{H}^2_\mathrm{diff}(\mathfrak{sl}(2), \mathcal{D}_{\barλ,μ})$, 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 $\mathcal{F}_μ$. |
| title | Second cohomology space of $\frak {sl}(2)$ acting on the space of $n$-ary differential operators on $\mathbb{R}$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2311.09199 |