  The link between (super)-affine Lie algebras as Poisson brackets structures
and integrable hierarchies provides both a classification and a tool for
obtaining superintegrable hierarchies. The lack of a fully systematic procedure
for constructing matrix-type Lax operators, which makes the supersymmetric case
essentially different from the bosonic counterpart, is overcome via the notion
of Poisson embeddings (P.E.), i.e. Poisson mappings relating affine structures
to conformal structures (in their simplest version P.E. coincide with the
Sugawara construction). A full class of hierarchies can be recovered by using
uniquely Lie-algebraic notions. The group-algebraic properties implicit in the
super-affine picture allow a systematic derivation of reduced hierarchies by
imposing either coset conditions or hamiltonian constraints (or possibly both).
