Stratifying systems over the hereditary path algebra with quiver $\mathbb{A}_{p,q}$

TL;DR

This paper constructs maximal stratifying systems with many regular elements over hereditary path algebras of type _{p,q}, extending previous bounds on the size of such systems.

Contribution

It explicitly constructs stratifying systems of size n with maximal regular elements over hereditary path algebras of type _{p,q}.

Findings

Constructed stratifying systems of size n with maximal regular elements.

Extended bounds on stratifying system sizes for hereditary algebras.

Provided explicit examples over _{p,q} quivers.

Abstract

The authors have proved in [J. Algebra Appl. 14 (2015), no. 6] that the size of a stratifying system over a finite-dimensional hereditary path algebra $A$ is at most $n$, where $n$ is the number of isomorphism classes of simple $A$-modules. Moreover, if $A$ is of Euclidean type a stratifying system over $A$ has at most $n-2$ regular modules. In this work, we construct a family of stratifying systems of size $n$ with a maximal number of regular elements, over the hereditary path algebra with quiver $\widetilde{\mathbb {A}}_{p,q} $, canonically oriented.