Mathematical Notes

, Volume 64, Issue 3, pp 342–346 | Cite as

Description of root systems with given Weyl group

  • I. I. Kotova
Article
  • 39 Downloads

Abstract

The paper is devoted to the description of generalized root systems with a given Weyl group. This problem arises in connection with the classification of infinite-dimensional Lie algebras and in the study of discrete groups generated by reflections. A criterion for the existence of a root system for a given discrete group generated by reflections and an algorithm of describing all root systems with a given Weyl group are obtained.

Key words

generalized root system Weyl group group generated by reflections Lie algebra Cartan subalgebra generalized Cartan matrix Kac-Moody algebra 

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References

  1. 1.
    V. G. Kac,Infinite Dimensional Lie Algebras, 3rd edition, Cambridge University Press, Cambridge (1993).Google Scholar
  2. 2.
    É. B. Vinberg, “Discrete linear groups that are generated by reflections,”Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],35, No. 5, 1072–1112 (1971).MATHMathSciNetGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • I. I. Kotova
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityUSSR

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