Lie bialgebra quantizations of the oscillator algebra and their universal $R$--matrices

Abstract

All coboundary Lie bialgebras and their corresponding Poisson--Lie structures are constructed for the oscillator algebra generated by $\{å,\ap,\am,\bb\}$. Quantum oscillator algebras are derived from these bialgebras by using the Lyakhovsky and Mudrov formalism and, for some cases, quantizations at both algebra and group levels are obtained, including their universal $R$--matrices.

19 pages, LaTeX; revised version to appear in J. Phys. A; quantization of bialgebras is completed

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