Exceptional realizations of the lorentz group: Supersymmetries and leptons

Abstract

Exceptional realizations of the Lorentz group are given via the exceptional Jordan algebra of Jordan, von Neumann and Wigner. The exceptionalSL2,C multiplets generate an intrinsically nonassociative algebra and have built in non-Abelian charge space properties. Considering these multiplets as the basis of a superspace it is shown how to give realizations of exceptional supersymmetry groups which incorporate important charge-space groups in a nontrivial way and which are different from the usual Clifford algebraic supersymmetry groups. Possible applications to the leptonic world are indicated.