# Cuspidal modules for the derivation Lie algebra over a rational quantum torus

## TL;DR

This paper provides an explicit description of cuspidal modules for the derivation Lie algebra over a rational quantum torus, including their structure and the action of the center, advancing understanding in quantum algebra representations.

## Contribution

It introduces a detailed structural characterization of cuspidal modules for derivation Lie algebras over rational quantum tori, incorporating the center's action.

## Key findings

- Explicit module structures characterized
- Inclusion of the center's action in the module description
- Enhanced understanding of derivation Lie algebra representations

## Abstract

Let $\mathbb C_Q$ denote a rational quantum torus with $d$ variables, and $\mathcal Z$ be the centre of $\mathbb C_Q$. In this paper we give a explicit description of the structure of the cuspidal modules for the derivation Lie algebra $\mathcal D$ over $\mathbb C_Q$, with an extra associative $\mathcal Z$-action.