Stratifying systems over hereditary algebras

TL;DR

This paper investigates the structure and limitations of stratifying systems over hereditary algebras, revealing bounds, existence, and non-existence results depending on the algebra's type and complexity.

Contribution

It provides new bounds for stratifying systems over tame hereditary algebras and constructs examples of complete systems over certain wild hereditary algebras.

Findings

Bound for size of stratifying systems over tame hereditary algebras

Existence of complete stratifying systems over wild hereditary algebras with more than 2 vertices

No stratifying systems with regular modules over certain hereditary algebras

Abstract

This paper deals with stratifying systems over hereditary algebras. In the case of tame hereditary algebras we obtain a bound for the size of the stratifying systems composed only by regular modules and we conclude that stratifying systems can not be complete. For wild hereditary algebras with more than 2 vertices we show that there exists a complete stratifying system whose elements are regular modules. In the other case, we conclude that there are no stratifing system over them with regular modules. In one example we built all the stratifying systems, with a specific form, having maximal number of regular summads.