$n$-angulated categories from self-injective algebras

TL;DR

This paper establishes conditions under which a $k$-linear category with an automorphism admits an $n$-angulated structure, providing new examples derived from self-injective algebras.

Contribution

It introduces a method to construct $n$-angulated categories from self-injective algebras using categorical automorphisms.

Findings

Existence of $n$-angulated structures under specific conditions

Construction of new $n$-angulated categories from self-injective algebras

Examples illustrating the theoretical framework

Abstract

Let $\mathcal{C}$ be a $k$-linear category with split idempotents, and $\Sigma:\mathcal{C}\rightarrow\mathcal{C}$ an automorphism. We show that there is an $n$-angulated structure on $(\mathcal{C},\Sigma)$ under certain conditions. As an application, we obtain a class of examples of $n$-angulated categories from self-injective algebras.