• DOI:10.1063/1.5009415
• Corpus ID: 119166123

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}
}

• S. Meljanac, Savsa Krevsi'c-Juri'c, Danijel Pikuti'c
• Published 20 October 2017
• Mathematics
• arXiv: Mathematical Physics

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.