Jacobi operators of quantum counterparts of three-dimensional real Lie algebras over the harmonic oscillator

TL;DR

This paper constructs quantum versions of three-dimensional real Lie algebras using operadic Lax representations for the harmonic oscillator and explicitly computes their Jacobi operators.

Contribution

It introduces a method to derive quantum Lie algebras from classical ones via operadic Lax representations, providing explicit calculations of their Jacobi operators.

Findings

Quantum counterparts of classical Lie algebras are constructed.

Jacobi operators for these quantum algebras are explicitly calculated.

The approach links harmonic oscillator dynamics with quantum algebra structures.

Abstract

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.