Standard components of a Krull-Schmidt category

TL;DR

This paper establishes criteria for when Auslander-Reiten components in Krull-Schmidt categories are standard, with applications to quiver representations, derived categories, and finite-dimensional algebras, revealing new standard components.

Contribution

It introduces new criteria for standardness of Auslander-Reiten components and applies them to various categories, including quiver representations and module categories.

Findings

Many new types of standard Auslander-Reiten components identified

Criteria established for components to be standard in Krull-Schmidt categories

Applications to finite-dimensional algebras and derived categories

Abstract

We provide criteria for an Auslander-Reiten component having sections of a Krull-Schmidt category to be standard. Specializing to the category of finitely presented representations of a strongly locally finite quiver and its bounded derived category, we obtain many new types of standard Auslander-Reiten components. An application to the module category of a finite-dimensional algebra yields some interesting results.