Algebras and Representation Theory

, Volume 16, Issue 1, pp 35–50

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

Open AccessArticle

DOI: 10.1007/s10468-011-9292-4

Cite this article as:
Basdouri, I. Algebr Represent Theor (2013) 16: 35. doi:10.1007/s10468-011-9292-4

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

CohomologyOrthosymplectic superalgebraSuperpseudodifferential operatorsPoisson 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