Harmonic Oscillator Lie Bialgebras and their Quantization

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.

8 pages, LaTeX; communication presented in the XXI ICGTMP, Goslar (Germany) 1996

Cited by in corpus (2)

• Cayley-Klein Lie bialgebras: Noncommutative spaces, Drinfel'd doubles and kinematical applications
• Darboux families and the classification of real four-dimensional indecomposable coboundary Lie bialgebras