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arXiv · hep-th/9310053

A generalization of the Jordan-Schwinger map: classical version and its q--deformation

V. I. Man'ko·G. Marmo·P. Vitale·F. Zaccaria
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Abstract

For all three--dimensional Lie algebras the construction of generators in terms of functions on 4-dimensional real phase space is given with a realization of the Lie product in terms of Poisson brackets. This is the classical Jordan--Schwinger map which is also given for the deformed algebras ${\cal {SL}}_{q}(2,\R)$, ${\cal E}_{q} (2)$ and ${\cal H}_q(1)$. The ${\cal U}_{q}(n)$ algebra is discussed in the same context.

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V. I. Man'ko, G. Marmo, P. Vitale, F. Zaccaria. 1993-10-08. A generalization of the Jordan-Schwinger map: classical version and its q--deformation. https://doi.org/10.1142/s0217751x94002260

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