The spaces $\mathrm{H}^n(\mathfrak{osp}(1|2),M)$ for some weight modules $M$

Didier Arnal (1) , Mabrouk Ben Ammar (2) , Bechir Dali (3)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 FSS - Faculté des Sciences de Sfax
3 Faculté des Sciences de Bizerte [Université de Carthage]

We entirely compute the cohomology for a natural and large class of $\mathfrak{osp}(1|2)$ modules $M$. We study the restriction to the $\mathfrak{sl}(2)$ cohomology of $M$ and apply our results to the module $M={\mathfrak D}_{\lambda,\mu}$ of differential operators on the super circle, acting on densities.

Mots clés: Cohomology; Lie superalgebra

Domaines: Algèbres quantiques [math.QA]

Didier Arnal, Mabrouk Ben Ammar, Bechir Dali. The spaces $\mathrm{H}^n(\mathfrak{osp}(1|2),M)$ for some weight modules $M$. Journal of Mathematical Physics, 2010, 51 (9), 15p. ⟨10.1063/1.3490194⟩. ⟨hal-00400827⟩