Hyperbolic subalgebras of hyperbolic Kac-Moody algebras
Anna Felikson, Pavel Tumarkin

TL;DR
This paper classifies regular hyperbolic subalgebras of hyperbolic Kac-Moody algebras by analyzing their Weyl groups, providing a finite algorithm for their classification and establishing subgroup relations.
Contribution
It introduces a finite algorithm to classify all regular hyperbolic subalgebras and establishes the correspondence between Weyl group subgroups and algebra subalgebras.
Findings
Classification of subgroup relations between Weyl groups.
Existence of algebra-subalgebra pairs for each subgroup relation.
Finite algorithm for classifying hyperbolic subalgebras.
Abstract
We investigate regular hyperbolic subalgebras of hyperbolic Kac-Moody algebras via their Weyl groups. We classify all subgroups relations between Weyl groups of hyperbolic Kac-Moody algebras, and show that for every pair of a group and subgroup their exists at least one corresponding pair of algebra and subalgebra. We also present a finite algorithm classifying all regular hyperbolic subalgebras of hyperbolic Kac-Moody algebras.
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