Defining an m-cluster category

TL;DR

This paper demonstrates that a specific orbit category captures the combinatorics of m-clusters, providing uniform proofs for key results in the simply laced cases, extending the understanding of cluster categories.

Contribution

It introduces a new orbit category that encodes m-cluster combinatorics, linking it to existing cluster categories and enabling uniform proofs.

Findings

Orbit category encodes m-cluster combinatorics

Provides type-uniform proofs for Fomin and Reading's results

Extends cluster category theory to m-clusters in simply laced cases

Abstract

We show that a certain orbit category considerd by Keller encodes the combinatorics of the $m$-clusters of Fomin and Reading in a fashion similar to the way the cluster category of Buan, Marsh, Reineke, Reiten, and Todorov encodes the combinatorics of the clusters of Fomin and Zelevinsky. This allows us to give type-uniform proofs of certain results of Fomin and Reading in the simply laced cases.