A geometric approach to Hall algebras I: Higher Associativity

TL;DR

This paper introduces a geometric framework that inherently satisfies higher associativity, enabling the categorification of Hall algebras and paving the way for constructing categorified representations.

Contribution

It presents a novel geometric approach to Hall algebras that naturally incorporates higher associativity, advancing their categorification and representation theory.

Findings

Constructed a geometric system recovering Hall algebra

Demonstrated higher associativity in the geometric framework

Outlined methods for categorified representation construction

Abstract

We construct a geometric system from which the Hall algebra can be recovered. This system inherently satisfies higher associativity conditions and thus leads to a categorification of the Hall algebra. We then suggest how to use this approach to construct categorified representations.