# On the Representation Dimension of Tame Cluster Tilted Algebras

## TL;DR

This paper investigates the representation dimension of tame cluster tilted algebras, establishing that their weak representation dimension is three and exploring conditions under which a constructed module determines the actual representation dimension.

## Contribution

It proves the weak representation dimension of tame cluster tilted algebras is three and identifies when a specific generator module determines the representation dimension.

## Key findings

- Weak representation dimension of tame cluster tilted algebras is three
- Constructed generator module reaches the weak representation dimension
- Conditions identified for the generator module to determine the representation dimension

## Abstract

The aim of this work is to study the representation dimension of cluster tilted algebras. We prove that the weak representation dimension of tame cluster tilted algebras is equal to three. We construct a generator module that reaches the weak representation dimension, unfortunately this module is not always a cogenerator. We show for which algebras this module gives the representation dimension.