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

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

1996-02-20

arxiv.org/abs/q-alg/9602029v2

J.Phys. A29 (1996) 4307-4320

Mathematics

Quantum Algebra

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

Scientific paper

10.1088/0305-4470/29/15/006

All coboundary Lie bialgebras and their corresponding Poisson--Lie structures
are constructed for the oscillator algebra generated by $\{\aa,\ap,\am,\bb\}$.
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.

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