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/