2-Kac-Moody algebras

TL;DR

This paper constructs a 2-category linked to Kac-Moody algebras, explores its 2-representations, and extends previous work on type A, connecting categorifications with K_0 properties.

Contribution

It introduces a new 2-category framework for Kac-Moody algebras and generalizes earlier type A results to broader classes.

Findings

Established a new 2-category associated with Kac-Moody algebras.

Analyzed the relationship between categorifications and 2-representations.

Extended previous type A categorification results to more general cases.

Abstract

We construct a 2-category associated with a Kac-Moody algebra and we study its 2-representations. This generalizes earlier work with Chuang for type A. We relate categorifications relying on K_0 properties and 2-representations.