Hyperbolic subalgebras of hyperbolic KAC-Moody algebras

摘要

We investigate regular hyperbolic subalgebras of hyperbolic Kac-Moody algebras via their Weyl groups. We classify all subgroup relations between Weyl groups of hyperbolic Kac-Moody algebras, and show that for every pair of a group and subgroup there exists at least one corresponding pair of algebra and subalgebra. We find all types of regular hyperbolic subalgebras for a given hyperbolic Kac-Moody algebra, and present a finite algorithm classifying all embeddings.