Classification of the d-representation-finite symmetric k-algebras of finite representation type

TL;DR

This paper classifies all symmetric Nakayama algebras and trivial extensions of path algebras that are finite in representation type, providing a comprehensive understanding of their structure over any field.

Contribution

It offers a complete classification of $d$-representation-finite symmetric Nakayama algebras and trivial extensions, extending to all symmetric algebras of finite type over algebraically closed fields.

Findings

Classified all $d$-representation-finite symmetric Nakayama algebras.

Classified all $d$-representation-finite trivial extensions of path algebras.

Provided a Morita equivalence classification over algebraically closed fields.

Abstract

We give a complete classification of all $d$-representation-finite symmetric Nakayama algebras and of all $d$-representation-finite trivial extensions of path algebras of quivers, over an arbitrary field. As a consequence we get a classification, up to Morita equivalence, of all $d$-representation-finite symmetric algebras of finite representation type over an algebraically closed field.