  We study the cohomology (cocycles) of Lie superalgebras for the generalised
complex of forms: superforms, pseudoforms and integral forms. We argue that
these cocycles might be interpreted in the light of a new brane scan as
generators of new higher-WZW terms and might provide new sources for
supergravity. We use the technique of spectral sequences to abstractly compute
the Chevalley-Eilenberg cohomology. We first focus on the superalgebra osp(2|2)
and show that there exist non-empty cohomology spaces among pseudoforms related
to sub-superalgebras. We then extend some classical theorems by Koszul to
include pseudoforms and integral forms. Further, we conjecture that the
Poincare' duality extends to Lie superalgebras, as long as all the complexes of
forms are taken into account and we prove that this holds for osp}(2|2). We
finally construct the cohomology representatives explicitly by using a
distributional realisation of pseudoforms and integral forms. On one hand,
these results show that the cohomology of Lie superalgebras is larger than
expected; on the other hand, we show the emergence of completely new cohomology
classes represented by pseudoforms. These classes represent integral form
classes of sub-superstructures.
