Algèbres de Lie semi-simples et affines

Michel Crétin

Publications du Département de mathématiques (Lyon) (1992)

  • Issue: 1, page 1-179
  • ISSN: 0076-1656

How to cite


Crétin, Michel. "Algèbres de Lie semi-simples et affines." Publications du Département de mathématiques (Lyon) (1992): 1-179. <>.

author = {Crétin, Michel},
journal = {Publications du Département de mathématiques (Lyon)},
language = {fre},
number = {1},
pages = {1-179},
publisher = {Université Claude Bernard - Lyon 1},
title = {Algèbres de Lie semi-simples et affines},
url = {},
year = {1992},

AU - Crétin, Michel
TI - Algèbres de Lie semi-simples et affines
JO - Publications du Département de mathématiques (Lyon)
PY - 1992
PB - Université Claude Bernard - Lyon 1
IS - 1
SP - 1
EP - 179
LA - fre
UR -
ER -


  1. Bourbaki N. [1] Groupes et algèbres de Lie, chap 4-6, Herman, Paris1968 Zbl0483.22001MR240238
  2. Bourbaki N. [2] Groupes et algèbres de Lie, chap 7-8, Herman, Paris1975 Zbl0483.22001
  3. Bruhat F., Tits J. [1] Groupes réductifs sur un corps local, IHES Pub Math. Zbl0254.14017
  4. Carter R.W. [1] Simple groups of Lie type, John Wiley, London1972 Zbl0723.20006MR407163
  5. Chevalley C. [1] Théorie des groupes de Lie, Groupes algébriques, théorèmes généraux sur les algèbres de Lie, Herman, Paris Zbl0186.33104
  6. Deodhar V.V. [1] Some characterizations of Coxeter groups, L'enseignement mathématique32 (1986), 111-120 Zbl0611.20030MR850554
  7. Dieudonne J. [1] Eléments d'analyse5, Gauthier-Villars1975 Zbl0303.43001
  8. Dixmier J. [1] Algèbres enveloppantes, Gauthier-Villars, Paris1974 Zbl0308.17007MR498737
  9. Frankel I.B., Kac V.G. [1] Basic representations of affine Lie algebras and dual resonance models, Inventiones Math62 (1980), 23-66 Zbl0493.17010MR595581
  10. Garland H. [1] The arithmetic theory of loop algebras, J. Algebra53, p 480-551, 1978 Zbl0383.17012MR502647
  11. Garland H. [2] The arithmetic theory of loop groups, IHES Pub. Math52, p 5-136, 1980 Zbl0475.17004MR601519
  12. Hee J.Y. [1] Groupe muni d'une donnée radicielle, Séminaire sur les groupes finis III, Pub Math Univ Paris VII, Paris1979 
  13. Jacobson N. [1] Lie algebras, Interscience, New-York1952 Zbl0121.27504MR143793
  14. Kac V.G. [1] Infinite dimensional Lie algebras, Cambridge University Press, Cambridge1985 Zbl0574.17010MR823672
  15. Kac V.G. [2] Constructing groups associated to infinite dimensionnal algebras, in Infinite dimensionnal groups with applications, p 167-216, MSRI, Springer Verlag, New York1985 Zbl0614.22006MR823320
  16. Kac V.G., Peterson D.H. [1] Defining relations of certains infinite dimensional groups. Astérisque, 1985 Zbl0625.22014MR837201
  17. Matsumoto H. [1] Sur les sous-groupes arithmétiques des groupes semi-simples déployés, Ann. scient. Ec. Norm. Sup.4° série, t 2, p 1-62, 1969 Zbl0261.20025MR240214
  18. Moody R. [1] A new class of Lie algebras, J. Algebra10 p 211-230, 1968 Zbl0191.03005MR229687
  19. Moody R., Teo K.L. [1] Tits systems with cristallographic Weyl groups, J. Algebra21, p 178-180, 1979 Zbl0232.20089MR320165
  20. Morita J. [1] Tits'systemes in Chevalley groupes over Laurent polynomial rings, Tsukuba J. Math, vol 3, N°2, p 41-51, 1979 Zbl0475.17005MR561845
  21. Peterson D.H., Kac V.G. [1] Infinite flag varieties and conjugacy theorems, Proc. Nat. Acad. Sci.USA, 80 (1983), 1778-1782 Zbl0512.17008MR699439
  22. Serre J.P. [1] Lie algebras and Lie groups, Benjamin, New-York et Amsterdam1965 Zbl0132.27803MR218496
  23. Serre J.P. [2] Algèbres de Lie semi-simples complexes, Benjamin, New-YorkAmsterdam1966 Zbl0144.02105MR215886
  24. Stein M.R. [1] Generators, relations and coverings of Chevalley groups over commutative rings, Amer. J. of Math., 93, p 969-1004, 1962 Zbl0246.20034MR322073
  25. Tits J. [1] Sur les constantes de structure et le théorème d'existence des algèbres de Lie semi-simples, IHES31 (1966), 21-58 Zbl0145.25804MR214638
  26. Tits J. [2] Normalisateurs de tores, I. Groupes de Coxeter étendus, Journal of algebra4 (1965), 96-116 Zbl0145.24703MR206117
  27. Tits J. [3] Groups and group functors attached to Kac-Moody data, Lectures notes in Math, vol 1111, p193-223, Springer1985 Zbl0572.17010MR797422
  28. Tits J. [4] Uniqueness and presentation of Kac-Moody groups over fields, Journal of algebra105 (1987), 542-573 Zbl0626.22013MR873684
  29. Varadarajan V.S. [11] Lie algebras and their representations, Springer Verlag, New-York1984 Zbl0955.22500MR746308

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