Indecomposable doubling for representations of the type I Lie superalgebras sl(m/n) and osp(2/2n)

We establish that for the type I Lie superalgebras sl(m/n) and osp(2/2n), each Kac module admits a 1 parameter family of indecomposable double extensions. The result follows from the explicit evaluation of the H¹ Lie superalgebra cohomology valued in the tensor product of the module and its dual.