Vertex operator construction of nonassociative algebras and their affinizations

Abstract

A general method for the vertex operator construction of nonassociative algebras and triple systems and their super analogs is given. Using this method the natural affine extensions of these algebraic structures can be defined and constructed. Essentially all the algebraic structures of physical theories based on ‘‘point particles’’ can be constructed this way. Conversely, these methods can be used to define the ‘‘stringy’’ analogs of these algebraic structures.