Embeddings of hyperbolic Kac-Moody algebras into $\mathbf{E_{10}}$}

TL;DR

This paper demonstrates that the hyperbolic Kac-Moody algebra E_{10} encompasses all simply laced hyperbolic Kac-Moody algebras as subalgebras, extending previous research methods.

Contribution

It introduces a new embedding technique showing E_{10} contains all simply laced hyperbolic Kac-Moody algebras as Lie subalgebras.

Findings

E_{10} contains all simply laced hyperbolic Kac-Moody algebras

Extension of Feingold and Nicolai's previous work

New embedding method for hyperbolic Kac-Moody algebras

Abstract

We show that the rank 10 hyperbolic Kac-Moody algebra $E_{10}$ contains every simply laced hyperbolic Kac-Moody algebra as a Lie subalgebra. Our method is based on an extension of earlier work of Feingold and Nicolai.