Skip to main content
Log in

Killing and the Coxeter transformation of Kac-Moody algebras

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Berman, S., Lee, Y.S., Moody, R.V.: The spectrum of a Coxeter transformation, Affine Coxeter Transformations and the Defect Map. J Algebra (to appear)

  2. Bourbaki, N.: Groupes et algèbres de Lie. Paris: Hermann 1968

    Google Scholar 

  3. A'Campo, N.: Sur les valeurs propres de la transformation de Coxeter. Invent. Math.33, 61–67 (1976)

    Google Scholar 

  4. Cartan, E.: Sur la structure des groupes de transformations finis et continus, Thèse, Paris, 1894; Oeuvres ComplètesI, 137–257 (1984)

  5. Cartan, E.: Les groupes projectifs, qui ne laissent invariantes aucune multiplicité plane. Bull. Soc. Math.41, 53–96 (1913); Oeuvres Complètes.I, 355–398 (1984)

    Google Scholar 

  6. Carter, R.: Simple groups of Lie type. New York: Wiley, 1972.

    Google Scholar 

  7. Coleman, A.J.: Curves on a surface. Am. Math. Mon.42, 212–220 (1940)

    Google Scholar 

  8. Coleman, A.J.: The Betti numbers of the simple Lie groups. Can. J. Math.10, 349–356 (1958)

    Google Scholar 

  9. Coleman, A.J.: The product of unitary reflections. Math. Reports, R. Soc. Can.6, 371–373 (1984)

    Google Scholar 

  10. Comtet, L.: Advanced combinatorics. Netherlands, Reidel 1974

    Google Scholar 

  11. Coxeter, H.S.M.: The product of the generators of a finite group generated by reflections. Duke. Math. J.18, 765–782 (1951)

    Google Scholar 

  12. Hawkins, T.: Wilhelm Killing and the structure of Lie algebras. Arch. Hist. Exact Sci.26, 127–192 (1982)

    Google Scholar 

  13. Howlett, R.B.: Coxeter groups andM-matrices. Bull. Lond. Math. Soc.14, 137–141 (1982)

    Google Scholar 

  14. Jordan, C.: Traité des substitutions. Paris: Gauthier-Villars 1870

    Google Scholar 

  15. Kac, V.: Simple graded Lie algebras of finite growth. Funct. Anal. Appl.1, 328–329 (1967)

    Google Scholar 

  16. Kac, V.: Infinite dimensional Lie algebras, 2nd ed. Camb. Univ. Press, 1985

  17. Killing, W.: Die Zusammensetzung der stetigen endlichen Transformationsgruppen. Math. Ann.,I.31, 252–290 (1888); II.33, 1–48 (1889); III.34, 57–122 (1989); IV.36, 161–189 (1890)

    Google Scholar 

  18. McConnell, A.J.: Applications of tensor analysis. New York: Dover 1957

    Google Scholar 

  19. Macdonald, I.G.: Kac-Moody algebras, Can. M. S. Proc., vol. 5, 1984 Conference on Lie Algebras and Related Topics, Britten, D.J., Lemire, F.W., Moody, R.V. (eds.): Am. Math. Soc. 69–109 (1984)

  20. Moody, R.V.: Lie algebras associated with generalized Cartan matrices. Bull. Am. Math. Soc.73, 217–221 (1967)

    Google Scholar 

  21. Senata, E.: Non-negative matrices and Markov chains (Theorem 1.5.). Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

  22. Steinberg, R.: Finite subgroups ofSU 2, Dynkin diagrams and affine coxeter elements. Pac. J. Math.118, 548–598 (1985)

    Google Scholar 

  23. Weyl, H.: The structure and representations of continuous groups. Inst. Ad. Study, Princeton Notes, 1935

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to H.S.M. Coxeter for his 80th Birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Coleman, A.J. Killing and the Coxeter transformation of Kac-Moody algebras. Invent Math 95, 447–477 (1989). https://doi.org/10.1007/BF01393885

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01393885

Keywords

Navigation