Existence of a 2-cluster tilting module does not imply finite complexity

TL;DR

This paper provides a counterexample showing that having a 2-cluster tilting module does not necessarily mean the algebra has finite complexity, challenging previous assumptions.

Contribution

It constructs a specific finite-dimensional algebra with a 2-cluster tilting module and infinite complexity, answering an open question.

Findings

Counterexample of algebra with 2-cluster tilting module and infinite complexity

Challenges previous assumptions linking 2-cluster tilting modules to finite complexity

Answers a question posed by Erdmann and Holm

Abstract

We give an example of a finite-dimensional algebra with a 2-cluster tilting module and a simple module which has infinite complexity. This answers a question of Erdmann and Holm.