Quantum counterparts of 3d Lie algebras over harmonic oscillator

TL;DR

This paper constructs quantum versions of 3d real Lie algebras using operadic Lax representations for the harmonic oscillator and computes their Jacobians, advancing the understanding of quantum algebra structures.

Contribution

It introduces a method to derive quantum counterparts of 3d Lie algebras via operadic Lax representations, which is a novel approach.

Findings

Quantum Lie algebras constructed from harmonic oscillator representations

Explicit calculations of Jacobians for the quantum algebras

New insights into the structure of quantum 3d Lie algebras

Abstract

Operadic Lax representations for the harmonic oscillator are used to construct the quantum counterparts of 3d real Lie algebras. The Jacobians of the corresponding quantum algebras are calculated.