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 $sl(m\mathrm{/}n)$ and $osp(2\mathrm{/}2n)$, each Kac module admits a 1 parameter family of indecomposable double extensions. The result follows from the explicit evaluation of the $H^1$ Lie superalgebra cohomology valued in the tensor product of the module and its dual.