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arxiv: q-alg/9701027 · v1 · pith:JQZLKT6Qnew · submitted 1997-01-27 · q-alg · math.QA

Harmonic Oscillator Lie Bialgebras and their Quantization

classification q-alg math.QA
keywords oscillatoralgebrabialgebraharmonicquantizationquantumbialgebrascoboundary
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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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