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Generalization of Weyl realization to a class of Lie superalgebras. (English) Zbl 1390.17010
Summary: 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 present 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.