# Generalization of Weyl realization to a class of Lie superalgebras

@article{Meljanac2017GeneralizationOW, title={Generalization of Weyl realization to a class of Lie superalgebras}, author={Stjepan Meljanac and Savsa Krevsi'c-Juri'c and Danijel Pikuti'c}, journal={arXiv: Mathematical Physics}, year={2017} }

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…

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