Inventiones mathematicae

, Volume 108, Issue 1, pp 323–347

Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy

  • S. Berman
  • R. V. Moody


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  1. [Be] Berman, S.: On generators and relations for certain involutory subalgebras of Kac-Moody Lie algebras. Commun. Algebra17 (12), 3165–3185 (1989)Google Scholar
  2. [BM] Benkart, G.M., Moody, R.V.: Derivations, central extensions and affine Lie algebras. Algebras Groups and Geom.3, 456–492 (1986)Google Scholar
  3. [Bo] Bourbaki, N.: Groupes et algèbres de Lie, Chap. IV, V, VI. Paris: Hermann 1968Google Scholar
  4. [Ca] Carter, R.W.: Simple Groups of Lie Type. London: Wiley 1972Google Scholar
  5. [Fa] Faulkner, J.R.: Barbilian Planes. Geom. Dedicata30, 125–181 (1989)Google Scholar
  6. [Ga] Garland, H.: The arithmetic theory of loop groups. Publ. Math., Inst. Hautes Étud. Sci.52, 5–136 (1980)Google Scholar
  7. [Hu] Humphreys, J.B.: Introduction to Lie algebras and representation theory. (Grad. Texts Math., vol. 9), Berlin Heidelberg New York: Springer 1972Google Scholar
  8. [Ka] Kassel, C.: Kähler Differentials and coverings of complex simple Lie algebras extended over a commutative ring. J. Pure Appl. Algebra34, 265–275 (1984)Google Scholar
  9. [KL] Kassel, C., Loday, J.-L.: Extensions centrales d'algèbres de Lie. Ann. Inst. Fourier32(4), 119–142 (1982)Google Scholar
  10. [MP] Moody, R., Pianzola, A.: Lie algebras with triangular decomposition. New York: J. Wiley 1992Google Scholar
  11. [MRY] Moody, R.V., Eswara Rao, S., Yokonuma, T.: Toroidal Lie algebras and vertex representations. Geom. Dedicata35, 283–307 (1990)Google Scholar
  12. [MY] Morita, J., Yoshii, Y.: Universal central extensions of Chevalley algebras over Laurent series polynomial rings and G.I.M. Lie algebras. Proc. Japan Acad., Ser. A61, 179–181 (1985)Google Scholar
  13. [PS] Pressley, A., Segal, G.: Loop groups. Oxford: Oxford University Press 1986Google Scholar
  14. [Sa] Santharoubane, L.J.: The second cohomology group for Kac-Moody Lie algebras and Kähler differentials. J. Algebra,125 (No. 1), 13–26 (1989)Google Scholar
  15. [Se] Seligman, G.: Rational methods in Lie algebras (Lect. Notes Pure Appl. Math.) New York: M. Dekker 1976Google Scholar
  16. [Sl1] Slodowy, P.: Beyond Kac-Moody algebras and inside. Can. Math. Soc. Conf. Proc.5, 361–371 (1986)Google Scholar
  17. [Sl2] Slodowy, P.: Singularitäten, Kac-Moody-Lie algebren, assoziierte Gruppen und Verallgemeinerungen. Habiliationsschrift, Universität Bonn (March 1984)Google Scholar
  18. [St] Steinberg, R.: Lectures on Chevalley Groups (notes by J. Faulkner and R. Wilson). Yale Univ. Lect. Notes (1967)Google Scholar
  19. [VdK] Van der Kallen, W.: Infinitesimally Central Extensions of Chevalley Groups. (Lect. Notes Math. vol. 356) Berlin Heidelberg New York: Springer 1973Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • S. Berman
    • 1
  • R. V. Moody
    • 2
  1. 1.Department of MathematicsUniversity of SaskatchewanSaskatoonCanada
  2. 2.Department of MathematicsUniversity of AlbertaEdmontonCanada

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