# The Nakayama automorphism of a self-injective preprojective algebra

## TL;DR

This paper provides a straightforward proof that certain preprojective algebras are Frobenius and describes their Nakayama automorphism using Auslander-Reiten theory.

## Contribution

It offers a simple proof of the Frobenius property and characterizes the Nakayama automorphism for preprojective algebras of finite type hereditary algebras.

## Key findings

- Preprojective algebra of finite type hereditary algebra is Frobenius
- The Nakayama automorphism is induced by the Nakayama functor
- Simplifies understanding of automorphisms in these algebras

## Abstract

We give a simple proof, using Auslander-Reiten theory, that the preprojective algebra of a basic hereditary algebra of finite representation type is Frobenius. We then describe its Nakayama automorphism, which is induced by the Nakayama functor on the module category of our hereditary algebra.