Generalization of Weyl realization to a class of Lie superalgebras

This paper generalizes Weyl realization to a class of Lie superalgebras $\mathfrak{ g}=\mathfrak{ g}_0\oplus \mathfrak{ g}_1$ satisfying $[\mathfrak{ g}_1,\mathfrak{ g}_1]=\{ 0\}$. First, we give a novel proof of the Weyl realization of a Lie algebra $\mathfrak{ g}_0$ 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.

Categories: math-ph hep-th math.MP