A quantum analogue of generalized cluster algebras

TL;DR

This paper introduces a quantum version of generalized cluster algebras, extending classical structural results to the quantum setting, particularly for rank two cases, broadening the understanding of quantum algebraic structures.

Contribution

It defines a quantum analogue of generalized cluster algebras and extends classical structural results to the quantum case for rank two.

Findings

Defined a quantum analogue of generalized cluster algebras.

Extended classical structural results to the quantum case for rank two.

Bridged classical and quantum cluster algebra theories.

Abstract

We define a quantum analogue of a class of generalized cluster algebras which can be viewed as a generalization of quantum cluster algebras defined in \cite{berzel}. In the case of rank two, we extend some structural results from the classical theory of generalized cluster algebras obtained in \cite{CS}\cite{rupel} to the quantum case.