The simplest non-associative generalization of supersymmetry

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.