Abstract
We compute the nth cohomology space of the affine Lie superalgebra aff(1) on the (1,1)dimensional real superspace with coefficient in a large class of aff(1)-modules M. We apply our results to the module of weight densities and the module of linear differential operators acting on a superspace of weighted densities. This work is the generalization of a result by Basdouri et al. [The linear aff(n vertical bar 1)-invariant differential operators on weighted densities on the superspace R-1 vertical bar n and aff(n vertical bar 1)-relative cohomology, Int. J. Geom. Meth. Mod. Phys. 10 (2013), Article ID: 1320004, 9 pp.]