Geodesic
Cohomology of osp(n|2) Acting on the Spaces of Linear Differential Operators on the Superspace R1|n
Nizar Ben Fraj1 ; Amina Jabeur2 ; Imen Safi2, 3, 4, 5, 6
1Institut Préparatoire aux Études d'Ingénieur, Université de Carthage, Campus Universitaire, 8000 Nabeul Merazka, Tunisia
2Dept. of Mathematics, Faculty of Sciences, University of Sfax, Route de Soukra -- B.P.802, 3018 Sfax, Tunisia
3We 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].
4Keywords: Invariant operators, cohomology, orthosymplectic superalgebra.
5MSC: 53D55, 14F10, 17B10, 17B68
6[
Journal of Lie Theory, Tome 23 (2013) no. 2, pp. 575-587

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

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

Nizar Ben Fraj  1   ; Amina Jabeur  2   ; Imen Safi  2 , 3 , 4 , 5 , 6

1 Institut Préparatoire aux Études d'Ingénieur, Université de Carthage, Campus Universitaire, 8000 Nabeul Merazka, Tunisia
2 Dept. of Mathematics, Faculty of Sciences, University of Sfax, Route de Soukra -- B.P.802, 3018 Sfax, Tunisia
3 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].
4 Keywords: Invariant operators, cohomology, orthosymplectic superalgebra.
5 MSC: 53D55, 14F10, 17B10, 17B68
6 [ 
Nizar Ben Fraj; Amina Jabeur; Imen Safi. Cohomology of osp(n|2) Acting on the Spaces of Linear Differential Operators on the Superspace R1|n. Journal of Lie Theory, Tome 23 (2013) no. 2, pp. 575-587. http://geodesic.mathdoc.fr/item/JOLT_2013_23_2_a10/
@article{JOLT_2013_23_2_a10,
     author = {Nizar Ben Fraj and Amina Jabeur and Imen 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},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2013_23_2_a10/}
}
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