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First Cohomology Space of the Orthosymplectic Lie Superalgebra \( \mathfrak{osp} \)(n|2) in the Lie Superalgebra of Superpseudodifferential Operators

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Ukrainian Mathematical Journal Aims and scope

We study the first cohomology space associated with the embedding of the Lie orthosymplectic superalgebra \( \mathfrak{osp} \)(n|2) on the (1,n)-dimensional superspace ℝ1|n in the Lie superalgebra \( \mathcal{S}\Psi \mathcal{DO} \)(n) (for n ≥ 4) of superpseudodifferential operators with smooth coefficients. Following Ovsienko and Roger, we present explicit expressions for the basis cocycles. We propose a simple generalization of a result obtained by Basdouri [Alg. Represent. Theory, 16, 35–50 (2013)].

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Authors and Affiliations

  1. Université de Sfax, Sfax, Tunisia

    M. Boujelben

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  1. M. Boujelben
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Correspondence to M. Boujelben.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 6, pp. 761–771, June, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i6.6052.

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Boujelben, M. First Cohomology Space of the Orthosymplectic Lie Superalgebra \( \mathfrak{osp} \)(n|2) in the Lie Superalgebra of Superpseudodifferential Operators. Ukr Math J 74, 871–882 (2022). https://doi.org/10.1007/s11253-022-02114-1

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  • DOI: https://doi.org/10.1007/s11253-022-02114-1

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