当前位置: X-MOL 学术Indian J. Pure Appl. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Cohomology of $${\mathfrak {sl}}(2)$$ sl ( 2 ) acting on the space of n-ary differential operators on $${\mathbb {R}}$$ R
Indian Journal of Pure and Applied Mathematics ( IF 0.7 ) Pub Date : 2021-07-12 , DOI: 10.1007/s13226-021-00012-z
Mabrouk Ben Ammar 1 , Rabeb Sidaoui 1
Affiliation  

We consider the spaces \({\mathcal {F}}_\mu\) of polynomial \(\mu\)-densities on the line as \({\mathfrak {sl}}(2)\)-modules and then we compute the cohomological spaces \(\text {H}^1_\text {diff}({\mathfrak {sl}}(2), {\mathcal {D}}_{{\bar{\lambda }},\mu })\), where \(\mu \in {\mathbb {R}}\), \({\bar{\lambda }}=(\lambda _1,\dots ,\lambda _n) \in {\mathbb {R}}^n\) and \({\mathcal {D}}_{{\bar{\lambda }},\mu }\) is the space of n-ary differential operators from \({\mathcal {F}}_{\lambda _1}\otimes \cdots \otimes {\mathcal {F}}_{\lambda _n}\) to \({\mathcal {F}}_\mu\).



中文翻译:

$${\mathfrak {sl}}(2)$$ sl ( 2 ) 的上同调作用于 $${\mathbb {R}}$$ R 上的 n 元微分算子的空间

我们将线上的多项式\(\mu\) -密度的空间\({\mathcal {F}}_\mu\)视为\({\mathfrak {sl}}(2)\) -modules 然后我们计算上同调空间\(\text {H}^1_\text {diff}({\mathfrak {sl}}(2), {\mathcal {D}}_{{\bar{\lambda }},\ mu })\) , 其中\(\mu \in {\mathbb {R}}\) , \({\bar{\lambda }}=(\lambda _1,\dots ,\lambda _n) \in {\ mathbb {R}} ^ N \)\({\ mathcal {d}} _ {{\酒吧{\拉姆达}},\亩} \)是空间ñ进制微分算子从\({\ mathcal {F}}_{\lambda _1}\otimes \cdots \otimes {\mathcal {F}}_{\lambda _n}\)\({\mathcal {F}}_\mu\)

更新日期:2021-07-12
down
wechat
bug