Cohomology of osp(n|2) Acting on the Spaces of Linear Differential Operators on the Superspace R<sup>1|n</sup>

N. Ben Fraj; A. Jabeur; I. Safi

Geodesic

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Cohomology of osp(n|2) Acting on the Spaces of Linear Differential Operators on the Superspace R^1|n

N. Ben Fraj ; A. Jabeur ; I. Safi

Journal of Lie theory, Tome 23 (2013) no. 2, pp. 575-587.

Voir la notice de l'article provenant de la source Heldermann Verlag

Résumé

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].

Classification : 53D55, 14F10, 17B10, 17B68
Mots-clés : Invariant operators, cohomology, orthosymplectic superalgebra

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     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},
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     volume = {23},
     number = {2},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JLT_2013_23_2_JLT_2013_23_2_a10/}
}

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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 R^1|n. Journal of Lie theory, Tome 23 (2013) no. 2, pp. 575-587. http://geodesic.mathdoc.fr/item/JLT_2013_23_2_JLT_2013_23_2_a10/