Static subcategories of the module category of a finite-dimensional hereditary algebra

TL;DR

This paper investigates how the classification of finite-dimensional modules over hereditary algebras relates to the subcategories of modules that are static with respect to indecomposable modules, aiming to characterize the algebra's representation type.

Contribution

It provides a characterization of the representation type of hereditary algebras based on subcategories of static modules associated with indecomposable modules.

Findings

Characterizes tame vs. wild representation types via static subcategories.

Establishes a link between module subcategories and algebra classification.

Offers new criteria for understanding hereditary algebra representations.

Abstract

Let k be a field, let A a finite-dimensional hereditary k-algebra. We consider the category of all finite-dimensional A-modules. We are going to characterize the representation type of A (tame or wild) in terms of the possible subcategories of all M-static modules, where M is an indecomposable A-module.