2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/50947It 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.LaTeX, 14 pages, added references and corrected some typos. To be published in Proc. of Int. Workshop ``Supersymmetries and Quantum Symmetries'', Sept. 21-25, 2001, Karpacz, PolandHigh Energy Physics - Theorytext