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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.
©2018 American Institute of Physics

MSC:
17A70 Superalgebras
11B68 Bernoulli and Euler numbers and polynomials
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