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

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 ${\mathcal{SL}}_q(2,\mathbb{R})$, ${\mathcal{E}}_q(2)$ and ${\mathcal{H}}_q(1)$. The ${\mathcal{U}}_q(n)$ algebra is discussed in the same context.

LATEX,21 pages,INFN-NA-IV-93/38,DSF-T-93/38

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