Relative cohomology spaces for some osp (n vertical bar 2)-modules

In this work, we describe the H-invariant, so(n)-relative cohomology of a natural class of osp (n vertical bar 2)-modules M, for n not equal 2. The Lie superalgebra osp (n vertical bar 2) can be realized as a superalgebra of vector fields on the superline R-1 vertical bar n. This yields canonical actions on spaces of densities and differential operators on the superline. The above result gives the zero, first, and second cohomology spaces for these modules of densities and differential operators. Published by AIP Publishing.