Quantum groups via Hall algebras of complexes

TL;DR

This paper presents a novel construction of quantum enveloping algebras of symmetric Kac-Moody Lie algebras using Hall algebras of Z_2-graded complexes of quiver representations over finite fields.

Contribution

It introduces a new finite field Hall algebra approach to realize quantum groups through complexes of quiver representations.

Findings

Constructs quantum groups from Hall algebras of complexes.

Establishes a connection between Kac-Moody algebras and quiver representations.

Provides a finite field algebraic framework for quantum group realization.

Abstract

We describe quantum enveloping algebras of symmetric Kac-Moody Lie algebras via a finite field Hall algebra construction involving Z_2-graded complexes of quiver representations.