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Hyperbolic subalgebras of hyperbolic Kac–Moody algebras

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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.

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Authors and Affiliations

  1. Independent University of Moscow, B. Vlassievskii 11, 119002, Moscow, Russia

    Anna Felikson & Pavel Tumarkin

  2. School of Engineering and Science, Jacobs University Bremen, Campus Ring 1, 28759, Bremen, Germany

    Anna Felikson & Pavel Tumarkin

Authors
  1. Anna Felikson
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  2. Pavel Tumarkin
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Correspondence to Anna Felikson.

Additional information

Research of both authors was supported in part by grant RFBR 11-01-00390-a and SNF projects 200020-113199 and 200020-121506/1.

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Felikson, A., Tumarkin, P. Hyperbolic subalgebras of hyperbolic Kac–Moody algebras. Transformation Groups 17, 87–122 (2012). https://doi.org/10.1007/s00031-011-9169-y

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  • DOI: https://doi.org/10.1007/s00031-011-9169-y

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