Abstract In [2](Preprint, 2006, arXiv: math. RT/0609363) the authors initiated a study of the
representation theory of classical Lie superalgebras via a cohomological approach.
Detecting subalgebras were constructed and a theory of support varieties was developed.
The dimension of a detecting subalgebra coincides with the defect of the Lie superalgebra,
and the dimension of the support variety for a simple supermodule was conjectured to equal
the atypicality of the supermodule. In this paper the authors compute the support varieties of …

Unlike Lie algebras, the finite dimensional complex representations of a simple Lie
superalgebra are usually not semisimple. As a consequence, despite over thirty years of
study, these remain mysterious objects. In this paper we introduce a new tool: the notion of
cohomological support varieties for the finite dimensional supermodules for a classical Lie
superalgebra $\mathfrak {g}=\mathfrak {g} _ {\bar 0}\oplus\mathfrak {g} _ {\bar 1} $ which are
completely reducible over ${\mathfrak g} _ {\bar 0} $. They allow us to provide a new …