Cohomology of aff(1|1) acting on the space of bilinear differential operators on the superspace IR1|1

We consider the aff(1)-module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the Lie superalgebra aff(1) with coefficients in space Dλ,ν;µ of bilinear differential operators acting on weighted densities. We study also the super analogue of this problem getting the same results.

Keywords:

Contact geometry , differential operators , Lie (super)algebra