Journal of Lie Theory

no. 2
Cohomology of osp(n|2) Acting on the Spaces of Linear Differential Operators on the Superspace R1|n
Journal of Lie Theory, Volume 23 (2013) no. 2, pp. 575-587
We compute the first differential cohomology of the orthosymplectic Lie superalgebra osp(n|2) with coefficients in the superspace of linear differential operators acting on the space of weighted densities on the (1,n)-dimensional real superspace. Likewise we compute its osp(n-1|2)-relative cohomology. We explicitly give 1-cocycles spanning these cohomology groups. This work is the simplest superization of a result by Lecomte [see: On the cohomology of sl(n+1,R) acting on differential operators and sl(n+1,R)-equivariant symbols, Indag. Math. NS. 11-1 (2000) 95--114].
DOI: 10.5802/jolt.738
Classification: 53D55, 14F10, 17B10, 17B68
Keywords: Invariant operators, cohomology, orthosymplectic superalgebra 
@article{JOLT_2013_23_2_a10,
     author = {N. Ben Fraj and A. Jabeur and I. Safi},
     title = {Cohomology of osp(n|2) {Acting} on the {Spaces} of {Linear} {Differential} {Operators} on the {Superspace} {R\protect\textsuperscript{1|n}}},
     journal = {Journal of Lie Theory},
     pages = {575--587},
     year = {2013},
     volume = {23},
     number = {2},
     doi = {10.5802/jolt.738},
     zbl = {1346.17011},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.738/}
}
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N. Ben Fraj; A. Jabeur; I. Safi. Cohomology of osp(n|2) Acting on the Spaces of Linear Differential Operators on the Superspace R1|n. Journal of Lie Theory, Volume 23 (2013) no. 2, pp. 575-587. doi: 10.5802/jolt.738

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