Cohomology of the Poisson superalgebra on spaces of superdimension (2, n_)

摘要

Under certain assumptions about the continuity of cochains, we study the cohomology spaces of a Poisson superalgebra, realized on the space of smooth Grassmann-valued functions with compact support in R-2. We find the zeroth, first, and second cohomology spaces in the adjoint representation in the case of a constant nondegenerate Poisson superbracket.