Second cohomology space of the orthosymplectic Lie superalgebra with coefficients in the Lie superalgebra of superpseudodifferential operators

We investigate the second cohomology space associated with the embedding of the orthosymplectic Lie superalgebra osp(n|2) on the (1,n)-dimensional superspace R1|n in the Lie superalgebra SΨDO(n) of superpseudodifferential operators with smooth coefficients, where n=0,1,2. We show that this space is purely even and we give explicit expressions of the basis cocycles.