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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