Operadic Lax representations for the harmonic oscillator are used to construct the quantum counterparts of three-dimensional real Lie algebras. The Jacobi operators of these quantum algebras are explicitly calculated.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-16, author = {Eugen Paal and J\"uri Virkepu}, title = {Jacobi operators of quantum counterparts of three-dimensional real Lie algebras over the harmonic oscillator}, journal = {Banach Center Publications}, volume = {95}, year = {2011}, pages = {199-209}, zbl = {1248.81042}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-16} }
Eugen Paal; Jüri Virkepu. Jacobi operators of quantum counterparts of three-dimensional real Lie algebras over the harmonic oscillator. Banach Center Publications, Tome 95 (2011) pp. 199-209. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-16/