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

Abstract : 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.
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Submitted on : Wednesday, July 1, 2009 - 7:30:20 PM
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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, American Institute of Physics (AIP), 2010, 51 (9), 15p. ⟨10.1063/1.3490194⟩. ⟨hal-00400827⟩

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