Transformation Groups

, 16:767 | Cite as

Root subsystems of loop extensions

Article
  • 57 Downloads

Abstract

We completely classify the real root subsystems of root systems of loop algebras of Kac–Moody Lie algebras. This classification involves new notions of “admissible subgroups” of the coweight lattice of a root system Ψ, and “scaling functions” on Ψ. Our results generalise and simplify earlier work on subsystems of real affine root systems.

References

  1. [1]
    N. Bourbaki, Groupes et Algèbres de Lie, Chapitres IV–VI, Actualités Scientifiques et Industrielles, No. 1337, Hermann, Paris, 1968. Russian transl.: Н. Бурбаки, Группы и алгебры Ли, гл. IV–VI, Мир, M., 1972.Google Scholar
  2. [2]
    M. J. Dyer, On rigidity of abstract root systems of Coxeter groups, arXiv:1011.2270 [math.GR], 2010.Google Scholar
  3. [3]
    M. J. Dyer, G. I. Lehrer, On reflection subgroups of finite and affine Weyl groups, Trans. Am. Math. Soc., to appear, 2011.Google Scholar
  4. [4]
    M. Dyer, Reflection subgroups of Coxeter systems, J. Algebra 135 (1990), no. 1, 57–73.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    M. Dyer, C. Bonnafé, Semidirect product decompositions of Coxeter groups, Comm. in Algebra 38 (2010), no. 4, 1549–1574.MATHCrossRefGoogle Scholar
  6. [6]
    V. G Kac, Infinite Dimensional Lie Algebras, Cambridge University Press, Cambridge, 1990. Russian transl.: В. Кац, Бесконечнометрные алгебры Ли, Мир, M., 1993.MATHCrossRefGoogle Scholar
  7. [7]
    R. V. Moody, A. Pianzola, Lie Algebras with Triangular Decompositions, Canadian Mathematical Society Series of Monographs and Advanced Texts, Wiley, New York, 1995.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics, 255 Hurley BuildingUniversity of Notre DameNotre DameUSA
  2. 2.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia

Personalised recommendations