, Volume 16, Issue 1, pp 35-50,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 30 Jun 2011

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


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.