Article

Algebras and Representation Theory

, Volume 16, Issue 1, pp 35-50

Open Access This content is freely available online to anyone, anywhere at any time.

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

  • Imed BasdouriAffiliated withDépartement de Mathématiques, Faculté des Sciences de Gafsa Tunisie Email author 

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