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Transformation Groups

, Volume 17, Issue 1, pp 87–122 | Cite as

Hyperbolic subalgebras of hyperbolic Kac–Moody algebras

  • Anna FeliksonEmail author
  • Pavel Tumarkin
Article

Abstract

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.

Keywords

Simplicial Group Maximal Subgroup Weyl Group Parabolic Subgroup Fundamental Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Independent University of MoscowMoscowRussia
  2. 2.School of Engineering and ScienceJacobs University BremenBremenGermany

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