  In the article at hand, we sketch how, by utilizing nilpotency to its fullest
extent (Engel, Super Engel) while using methods from the theory of universal
enveloping algebras, a complete description of the indecomposable
representations may be reached. In practice, the combinatorics is still
formidable, though.
  It turns out that the method applies to both a class of ordinary Lie algebras
and to a similar class of Lie superalgebras.
  Besides some examples, due to the level of complexity we will only describe a
few precise results. One of these is a complete classification of which ideals
can occur in the enveloping algebra of the translation subgroup of the
Poincar\'e group. Equivalently, this determines all indecomposable
representations with a single, 1-dimensional source. Another result is the
construction of an infinite-dimensional family of inequivalent representations
already in dimension 12. This is much lower than the 24-dimensional
representations which were thought to be the lowest possible. The complexity
increases considerably, though yet in a manageable fashion, in the
supersymmetric setting. Besides a few examples, only a subclass of ideals of
the enveloping algebra of the super Poincar\'e algebra will be determined in
the present article.
