Cluster tilting modules for local algebras

TL;DR

This paper presents the first example of a non-trivial cluster tilting module in a local finite-dimensional algebra, using explicit calculations with the GAP QPA package to analyze the higher Auslander algebra.

Contribution

It provides the first known example of a non-trivial cluster tilting module in a local algebra and details the explicit computation of the associated higher Auslander algebra.

Findings

Explicit example of a non-trivial cluster tilting module in local algebra

Calculation of higher Auslander algebra via quiver and relations

Discussion of related problems and conjectures

Abstract

We give the first example of a non-trivial cluster tilting module in a local finite dimensional algebra. To do this, we give an explicit calculation of the corresponding higher Auslander algebra by quiver and relations using the GAP-package QPA. We discuss related problems and conjectures for local finite-dimensional algebras.