Realizing orbit categories as stable module categories - a complete classification

TL;DR

This paper provides a complete classification of certain triangulated orbit categories of path-algebras of Dynkin diagrams, showing they correspond to stable module categories of specific self-injective algebras, with explicit descriptions.

Contribution

It offers a full classification and explicit descriptions of triangulated orbit categories as stable module categories for representation-finite self-injective algebras.

Findings

Classified all such orbit categories up to triangle equivalence.

Provided explicit algebraic descriptions for each classified category.

Connected orbit categories with stable module categories of self-injective algebras.

Abstract

We classify all triangulated orbit categories of path-algebras of Dynkin diagrams that are triangle equivalent to a stable module category of a representation-finite self-injective standard algebra. For each triangulated orbit category T we give an explicit description of a representation-finite self-injective standard algebra with stable module category triangle equivalent to T.