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Harmonic Oscillator Lie Bialgebras and their Quantization

Angel Ballesteros·Francisco J. Herranz
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Abstract

All possible Lie bialgebra structures on the harmonic oscillator algebra are explicitly derived and it is shown that all of them are of the coboundary type. A non-standard quantum oscillator is introduced as a quantization of a triangular Lie bialgebra, and a universal $R$-matrix linked to this new quantum algebra is presented.

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Angel Ballesteros, Francisco J. Herranz. 1997-01-27. Harmonic Oscillator Lie Bialgebras and their Quantization. https://arxiv.org/abs/q-alg/9701027

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