A class of Lorentzian Kac-Moody algebras

TL;DR

This paper introduces a new class of Lorentzian Kac-Moody algebras, detailing their properties, construction, and potential role as symmetries in M-theory and string theory.

Contribution

It generalizes hyperbolic Kac-Moody algebras to Lorentzian cases, providing conditions, fundamental weights, and analysis of subalgebras, expanding the mathematical framework for theoretical physics.

Findings

Identified conditions for Lorentzian structure

Constructed fundamental weights of the algebras

Analyzed the presence of real principal so(1,2) subalgebras

Abstract

We consider a natural generalisation of the class of hyperbolic Kac-Moody algebras. We describe in detail the conditions under which these algebras are Lorentzian. We also construct their fundamental weights, and analyse whether they possess a real principal so(1,2) subalgebra. Our class of algebras include the Lorentzian Kac-Moody algebras that have recently been proposed as symmetries of M-theory and the closed bosonic string.