Mathematical Notes

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

Description of root systems with given Weyl group

  • I. I. Kotova


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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  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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