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.
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Basdouri, I. First Space Cohomology of the Orthosymplectic Lie Superalgebra in the Lie Superalgebra of Superpseudodifferential Operators. Algebr Represent Theor 16, 35–50 (2013). https://doi.org/10.1007/s10468-011-9292-4
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DOI: https://doi.org/10.1007/s10468-011-9292-4