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Generalized Grassmann Algebras and its Connection to the Extended Supersymmetric Models

A. P. Isaev·Z. Popowicz·O. Santillan
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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.

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A. P. Isaev, Z. Popowicz, O. Santillan. 2002-01-08. Generalized Grassmann Algebras and its Connection to the Extended Supersymmetric Models. https://arxiv.org/abs/hep-th/0110246

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