First space cohomology of the orthosymplectic lie superalgebra in the lie superalgebra of superpseudodifferential operators

摘要

We investigate the first cohomology space associated with the embedding of the Lie Orthosymplectic superalgebra osp(n|2) on the (1,n)-dimensional superspace ?1|n in the Lie superalgebra SΨDO(n) of superpseudodifferential operators with smooth coefficients, where n = 0, 1, 2. Following Ovsienko and Roger, we give erxplicit expressions of the basis cocycles.