# Example of categorification of a cluster algebra

## TL;DR

This paper provides detailed examples of how cluster algebras associated with coordinate rings of unipotent subgroups can be categorified, illustrating the process for both simply-laced and non-simply-laced types.

## Contribution

It introduces explicit additive categorifications for cluster algebra structures in specific Lie group cases, making the concepts more accessible.

## Key findings

- Categorification of $A_3$ cluster algebra using Geiß-Leclerc-Schröer approach
- Categorification of $C_2$ cluster algebra based on author's work
- Accessible explanations for non-experts in the field

## Abstract

We present here two detailed examples of additive categorifications of the cluster algebra structure of a coordinate ring of a maximal unipotent subgroup of a simple Lie group. The first one is of simply-laced type ($A_3$) and relies on an article by Gei\ss, Leclerc and Schr\"oer. The second is of non simply-laced type ($C_2$) and relies on an article by the author of this note. This is aimed to be accessible, specially for people who are not familiar with this subject.