The simplest non-associative generalization of supersymmetry

TL;DR

This paper proposes a nonassociative extension of supersymmetry, exploring algebraic structures like associators and Jacobiators to understand potential physical implications and connections to hidden variables.

Contribution

It introduces the simplest form of nonassociative supersymmetry by deriving 3- and 4-point associators based on zero Jacobiators, expanding the algebraic framework.

Findings

Derived the simplest 3-point associators for supersymmetric generators.

Established a connection between 3- and 4-point associators.

Calculated Jacobiators for products of four generators.

Abstract

Nonassociative generalization of supersymmetry is suggested. 3- and 4-point associators for supersymmetric generators are considered. On the basis of zero Jacobiators for three supersymmetric generators, we have obtained the simplest form of 3-point associators. The connection between 3- and 4-point associators is considered. On the basis of this connection, 4-point associators are obtained. The Jacobiators for the product of four supersymmetric generators are calculated. We discuss the possible physical meaning of numerical coefficients presented on the right-hand sides of associators. The possible connection between supersymmetry, hidden variables, and nonassociativity is discussed.