Representations of Thread Quivers

TL;DR

This paper introduces thread quivers, a new infinite generalization of quivers, and demonstrates their use in explicitly constructing a broad class of hereditary categories with Serre duality.

Contribution

It defines thread quivers and proves their equivalence to certain hereditary categories, providing a new explicit construction method.

Findings

Every hereditary category with Serre duality is equivalent to finitely presented representations of a thread quiver.

Thread quivers generalize classical quivers to infinite settings.

New class of hereditary categories with explicit construction.

Abstract

We introduce thread quivers as an (infinite) generalization of quivers, and show that every k-linear (k algebraically closed) hereditary category with Serre duality and enough projectives is equivalent to the category of finitely presented representations of a thread quiver. In this way, we obtain an explicit construction of a new class of hereditary categories with Serre duality.