The existence of greedy bases in rank 2 quantum cluster algebras

TL;DR

This paper proves that rank 2 quantum cluster algebras possess a quantum version of the greedy basis, extending classical cluster algebra concepts into the quantum setting.

Contribution

It introduces a quantum lift of the greedy basis, providing a new foundational element for quantum cluster algebra theory.

Findings

Existence of a quantum greedy basis in rank 2 quantum cluster algebras

Extension of classical greedy basis to quantum setting

Foundational step for further quantum cluster algebra research

Abstract

We establish the existence of a quantum lift of the greedy basis.