TL;DR
This paper introduces cluster characters within 2-Calabi-Yau triangulated categories, explaining their properties and role in categorifying cluster algebras, based on lecture notes from a 2016 mini-course.
Contribution
It provides an accessible introduction to cluster characters, connecting F-polynomials, cluster categories, and 2-Calabi-Yau categories for categorification purposes.
Findings
Defines cluster characters and their properties
Links cluster characters to categorification of cluster algebras
Provides foundational knowledge for further research in the area
Abstract
These are lecture notes from a mini-course given at the CIMPA 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.
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Taxonomy
TopicsCatalysis and Oxidation Reactions