FIRST COHOMOLOGY SPACE OF THE ORTHOSYMPLECTIC LIE SUPERALGEBRA osp(n2) IN THE LIE SUPERALGEBRA OF SUPERPSEUDODIFFERENTIAL OPERATORS

摘要

We study the first cohomology space associated with the embedding of the Lie orthosymplectic superalgebra osp(n2) on the (1, n)-dimensional superspace R1n in the Lie superalgebra S DO(n) (for n = 4) of superpseudodifferential operators with smooth coefficients. Following Ovsienko and Roger, we present explicit expressions for the basis cocycles. We propose a simple generalization of a result obtained by Basdouri Alg. Represent. Theory, 16, 35-50 (2013).