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Cohomology of orthosymplectic Lie superalgebra acting on $λ$ -densities on $ℝ^{1 | n}$

Département de Mathématiques, Faculté des Sciences de Sfax, Université de Sfax, laboratoire Algebra Geometry and Theory Spectral, BP 802, Sfax 3038, Tunisie

E-mail Address: nabilagomdi@hotmail.fr

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and

Rim Messaoud

Département de Mathématiques, Faculté des Sciences de Gafsa, Université de Gafsa, Laboratoire Algebra Geometry and Theory Spectral, Zarroug 2112, Gafsa, Tunisie

E-mail Address: rimessaoud@yahoo.fr

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https://doi.org/10.1142/S0219887817500165Cited by:2 (Source: Crossref)

Abstract

We compute the first differential cohomology of the orthosymplectic Lie superalgebra $𝔬 𝔰 𝔭 (n | 2)$ with coefficients in the superspace of weighted densities $𝔉_{λ}^{n}$ on the (1, 2)-dimensional real superspace. We explicitly give 1-cocycles spanning these cohomologies. This work is the simplest generalization of a result by Basdouri and Essayari [On cohomology of the orthosymplectic superalgebra, Acta Math. Hungar.130(1–2) (2011) 155–166].

Keywords:

AMSC: 17B56, 53D55, 58H15

References

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