---
abstract: 'These are lecture notes from a mini-course given at the CIMPA school in Mar del Plata, Argentina, in March 2016. The aim of the course was to introduce cluster characters for $2$-Calabi–Yau triangulated categories and present their main properties. The notes start with the theory of $F$-polynomials of modules over finite-dimensional algebras. Cluster categories are then introduced, before the more general setting of $2$-Calabi–Yau triangulated categories with cluster-tilting objects is defined. Finally, cluster characters are presented, and their use in the categorification of cluster algebras is outlined.'
address: 'Laboratoire de Mathématiques d’Orsay, Univ. Paris-Sud, CNRS, Univ. Paris-Saclay, 91405 Orsay, France'
author:
- 'Pierre-Guy Plamondon'
title: Cluster characters
---

[^1]

Introduction
============

Shortly after the introduction of cluster algebras in [@FZ02], links with an impressively vast number of fields of mathematics were uncovered. Among these is the representation theory of finite-dimensional algebras, whose links to cluster algebras became apparent in, for instance, [@MRZ03], [@BMRRT06], [@CC06], ...

The link between representation theory and cluster algebra has proved itself to be fruitful on both sides: on the one hand, it has allowed an understanding of cluster algebras that has led to the proof of conjectures of Fomin and Zelevinsky: see for 