# $n$-cluster tilting subcategories of representation-directed algebras

## TL;DR

This paper characterizes $n$-cluster tilting subcategories in representation-directed algebras using $n$-Auslander-Reiten translations and classifies certain Nakayama algebras with these properties.

## Contribution

It provides a new characterization of $n$-cluster tilting subcategories and classifies specific classes of Nakayama algebras with such subcategories.

## Key findings

- Characterization of $n$-cluster tilting subcategories via $n$-Auslander-Reiten translations
- Classification of acyclic Nakayama algebras with homogeneous relations admitting $n$-cluster tilting
- Classification of Nakayama algebras with finite global dimension admitting $d$-cluster tilting

## Abstract

We give a characterization of $n$-cluster tilting subcategories of representation-directed algebras based on the $n$-Auslander-Reiten translations. As an application we classify acyclic Nakayama algebras with homogeneous relations which admit an $n$-cluster tilting subcategory. Finally, we classify Nakayama algebras of global dimension $d<\infty$ which admit a $d$-cluster tilting subcategory.