  It is shown that the fermionic Heisenberg-Weyl algebra with 2N=D fermionic
generators is equivalent to the generalized Grassmann algebra with two
fractional generators. The 2,3 and 4 dimensional Heisenberg - Weyl algebra is
explicitly given in terms of the fractional generators. These algebras are used
for the formulation of the N=2,3,4 extended supersymmetry. As an example we
reformulate the Lax approach of the supersymmetric Korteweg - de Vries equation
in terms of the generators of the generalized Grassmann algebra.
