Algebras and Representation Theory

, Volume 16, Issue 1, pp 35–50 | Cite as

First Space Cohomology of the Orthosymplectic Lie Superalgebra in the Lie Superalgebra of Superpseudodifferential Operators

Open Access
Article

Abstract

We investigate 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 \( \mathcal{S}\Psi\mathcal{DO}(n)\) of superpseudodifferential operators with smooth coefficients, where n = 0, 1, 2. Following Ovsienko and Roger, we give erxplicit expressions of the basis cocycles.

Keywords

Cohomology Orthosymplectic superalgebra Superpseudodifferential operators Poisson superalgebra 

Mathematics Subject Classification (2010)

53D55 

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Département de MathématiquesFaculté des Sciences de Gafsa TunisieZarrougTunisia

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