English

Generalized Grassmann Algebras and its Connection to the Extended Supersymmetric Models

High Energy Physics - Theory 2007-05-23 v2

Abstract

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.

Keywords

Cite

@article{arxiv.hep-th/0110246,
  title  = {Generalized Grassmann Algebras and its Connection to the Extended Supersymmetric Models},
  author = {A. P. Isaev and Z. Popowicz and O. Santillan},
  journal= {arXiv preprint arXiv:hep-th/0110246},
  year   = {2007}
}

Comments

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, Poland