Cohomology of aff(2) acting on some modules and deformations

Over the (1, 2)-dimensional real superspace, we compute the cohomology space of the affine Lie superalgebra aff(2) with coefficient in a large class of aff(2)-modules M. We apply our results to the module M = delta(Omega)(lambda). of weight densities and the module M = D-lambda,mu(2) of linear differential operators acting on a superspace of weighted densities. We study nontrivial deformations of the natural action of the Lie superalgebra aff(2) on the direct sum of the superspaces of weighted densities.