  We investigate a new cohomology of Lie superalgebras, which may be compared
to a de Rham cohomology of Lie supergroups involving both differential and
integral forms. It is defined by a BRST complex of Lie superalgebra modules,
which is formulated in terms of a Weyl superalgebra and incorporates
inequivalent representations of the bosonic Weyl subalgebra. The new cohomology
includes the standard Lie superalgebra cohomology as a special case. Examples
of new cohomology groups are computed.
