Cluster characters for cluster categories with infinite-dimensional morphism spaces

TL;DR

This paper establishes the existence of cluster characters in Hom-infinite cluster categories, introduces a mutation-invariant subcategory, and discusses applications to categorify skew-symmetric cluster algebras.

Contribution

It provides the first construction of cluster characters for Hom-infinite categories and introduces a mutation-invariant subcategory for this purpose.

Findings

Existence of cluster characters in Hom-infinite cluster categories

Introduction of a mutation-invariant subcategory

Framework for categorifying skew-symmetric cluster algebras

Abstract

We prove the existence of cluster characters for Hom-infinite cluster categories. For this purpose, we introduce a suitable mutation-invariant subcategory of the cluster category. We sketch how to apply our results in order to categorify any skew-symmetric cluster algebra. More applications and a comparison to Derksen-Weyman-Zelevinsky's results will be given in a future paper.