Irreducible Modules for the loop of Derivations of Rational Quantum Torus

TL;DR

This paper classifies irreducible modules for the loop of derivations of rational quantum tori, focusing on their associative and anti-associative actions, advancing understanding in quantum algebra representations.

Contribution

It provides a complete classification of irreducible modules for a specific quantum algebra structure, detailing their associative and anti-associative actions.

Findings

Classified irreducible modules for the loop of derivations of rational quantum tori.

Described the module actions as associative and anti-associative.

Enhanced the understanding of quantum algebra representations.

Abstract

In this paper we classified irreducible modules for the loop of derivations of rational quantum torus with associative $\mathbb{C}_q^1\otimes B$ action and anti-associative $\mathbb{C}_q^2\otimes B$ action on the modules.