The Hall algebra of a cyclic quiver at $q=0$

TL;DR

This paper demonstrates that the Hall algebra of nilpotent representations of a cyclic quiver at q=0 is isomorphic to Reineke's extension monoid, extending previous work in the field.

Contribution

It establishes an isomorphism between the Hall algebra at q=0 and the extension monoid for cyclic quivers, advancing the understanding of their algebraic structures.

Findings

Hall algebra at q=0 is isomorphic to the extension monoid

Extends Reineke's previous work on Hall algebras

Provides a new perspective on representations of cyclic quivers

Abstract

We show that the generic Hall algebra of nilpotent representations of an oriented cycle specialised at $q=0$ is isomorphic to the generic extension monoid in the sense of Reineke. This continues the work of Reineke.