# 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}
}
• 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…
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We introduce the generalized Heisenberg algebra $\mathcal{H}_n$ and construct realizations of the orthogonal and Lorentz algebras by power series in a semicompletion of $\mathcal{H}_n$. The obtained
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• 2022
Symmetric ordering and Weyl realizations for non-commutative quantum Minkowski spaces are reviewed. Weyl realizations of Lie deformed spaces and corresponding star products, as well as twist
(2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p

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