Generalization of Weyl realization to a class of Lie superalgebras

Abstract

This paper generalizes Weyl realization to a class of Lie superalgebras g=g0 g1 satisfying [g1,g1]={0}. First, we present a novel proof of the Weyl realization of a Lie algebra g0 by deriving a functional equation for the function that defines the realization. We show that this equation has a unique solution given by the generating function for the Bernoulli numbers. This method is then generalized to Lie superalgebras of the above type.