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

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.

10 pages. to appear in Letters in Mathematical Physics

References in corpus (6)

• E10 and a "small tension expansion" of M Theory
• E_(10), BE_(10) and Arithmetical Chaos in Superstring Cosmology
• E10 and SO(9,9) invariant supergravity
• Higher order M theory corrections and the Kac-Moody algebra E10
• Hyperbolic Kac Moody Algebras and Einstein Billiards
• E10 Cosmology

Cited by in corpus (4)

• Hyperbolic Weyl groups and the four normed division algebras
• Automorphic correction of the hyperbolic Kac-Moody algebra $E_{10}$
• Hyperbolic subalgebras of hyperbolic Kac-Moody algebras
• $\pi$-systems and the embedding problem for rank $2$ Kac-Moody Lie algebras