Generalization of Weyl realization to a class of Lie superalgebras
| Autor: | Stjepan Meljanac, Saša Krešić-Jurić, Danijel Pikutić |
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| Rok vydání: | 2017 |
| Předmět: |
High Energy Physics - Theory
Pure mathematics 010308 nuclear & particles physics Generating function FOS: Physical sciences Statistical and Nonlinear Physics Function (mathematics) Mathematical Physics (math-ph) Type (model theory) 01 natural sciences Mathematics::Group Theory Number theory High Energy Physics - Theory (hep-th) 0103 physical sciences Functional equation Lie algebra Weyl realization Lie superalgebras noncommutative spaces 010306 general physics Mathematics::Representation Theory Realization (systems) Bernoulli number Mathematical Physics Mathematics |
| Zdroj: | Journal of Mathematical Physics |
| DOI: | 10.48550/arxiv.1710.07494 |
| Popis: | 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. Comment: 13 pages |
| Databáze: | OpenAIRE |
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