E10 for beginners

  • R.W. GebertEmail author
  • H. NicolaiEmail author
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 447)


Vertex Operator Dynkin Diagram Transversal State Root Space String Vertex Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    R. E. Borcherds. Vertex algebras, Kac-Moody algebras, and the monster. Proceedings of the National Academic Society USA, 83:3068–3071,1986.Google Scholar
  2. 2.
    R. E. Borcherds. Generalized Kac-Moody algebras. Journal of Algebra,115:501–512,1988.Google Scholar
  3. 3.
    R. E. Borcherds. The monster Lie algebra. Advances in Mathematics, 83:30–47, 1990.Google Scholar
  4. 4.
    R. C. Brower. Spectrum-generating algebra and no-ghost theorem for the dual model. Physical Review, D6:1655–1662,1972.Google Scholar
  5. 5.
    J. H. Conway. The automorphism group of the 26-dimensional even unimodular Lorentzian lattice. Journal of Algebra, 80:159–163, 1983.Google Scholar
  6. 6.
    E. Del Giudice, P Di Vecchia, and S. Fubini. General properties of the dual resonance model. Annals of Physics, 70:378–398,1972.Google Scholar
  7. 7.
    A. J. Feingold and I. B. Frenkel. A hyperbolic Kac-Moody algebra and the theory of Siegel modular forms of genus 2. Mathernatische Annalen, 263:87–144,1983.Google Scholar
  8. 8.
    I. B. Frenkel. Representations of Kac-Moody algebras and dual resonance models. In Applications of Group Theory in Theoretical Physics, pages 325–353, American Mathematical Society, Providence, 1985. Lect. Appl. Math., Vol. 21.Google Scholar
  9. 9.
    I. B. Frenkel and V. G. Kac. Basic representations of affine Lie algebras and dual models. Inventiones Mathematicae, 62:23–66,1980.Google Scholar
  10. 10.
    I. B. Frenkel, J. Lepowsky, and A. Meurtan. Vertex Operator Algebras and the Monster. Pure and Applied Mathematics Volume 134, Academic Press, San Diego, 1988.Google Scholar
  11. 11.
    R. W. Gebert. Introduction to vertex algebras, Borcherds algebras, and the monster Lie algebra. International Journal of Modern Physics, A8:5441–5503, 1993.Google Scholar
  12. 12.
    R.W. Gebert and H. Nicolai. On E 10 and the DDF construction, to appear m Communications in Mathematical Physics.Google Scholar
  13. 13.
    P Goddard, A. Kent, and D. Olive. Virasoro algebras and coset space models. Physics Letters, 152 B:88–92,1985Google Scholar
  14. 14.
    P Goddard and D. Olive. Algebras, lattices and strings. In J. Lepowsky, S. Mandelstam, and I. M. Singer, editors, Vertex Operators in Mathematics and Physics-Proceedings of a Conference November 10-17, 1983, pages 51–96, Springer, New York, 1985. Publications of the Mathematical Sciences Research Institute #3.Google Scholar
  15. 15.
    P. Goddard and D. Olive. Kac-Moodyand Virasoro algebras in relation to quantum physics. International Journal of Modern Physics, A 1:303–414,1986.Google Scholar
  16. 16.
    M. B. Green, J. H. Schwarz, and E. Witten. Superstring Theory Vol. 1&2. Cambridge University Press, 1988.Google Scholar
  17. 17.
    D. J. Gross. High-energy symmetries of string theory. Physical Review Letters, 60:1229–1232,1988.Google Scholar
  18. 18.
    C. M. Hull, and P K. Townsend. Unity of Superstring Dualities. preprint QMW-94-30, R/94/33, 1994.Google Scholar
  19. 19.
    B. Julia. in: Superspace and Supergravity, eds. S. W. Hawking and M. Rocek Cambridge University Press, 1981: Lectures in Applied Mathematics, 21: 355–373,1985.Google Scholar
  20. 20.
    B. Julia and H. Nicolai. Null-Killing Vector Dimensional Reduction and Galilean preprint LPTENS 94/21, DESY 94-156,1994.Google Scholar
  21. 21.
    V. G. Kac. Infinite dimensional Lie algebras. Cambridge University Press, Cambridge, third edition, 1990.Google Scholar
  22. 22.
    V. G. Kac, R. V. Moody, and M. Wakimoto. On E 10. In K. Bleuler and M. Werner editors, Differential geometrical methods in theoretical physics. Proceedings, NATO advanced research workshop, 16th international conference, Como, pages 109–128, Kluwer, 1988.Google Scholar
  23. 23.
    S. Kass, R. V. Moody, J. Patera, and R. Slansky. Affine Lie Algebras, Weight Multiplicities, andBranching Rules, Volume 1& 2. University of California Press, Berkeley, 1990.Google Scholar
  24. 24.
    G. Moore. Finite in all directions. preprint HEP-TH/9305139, YCTP-P12-93, Yale University, New Haven,1993.Google Scholar
  25. 25.
    H. Nicolai. Physics Letters, B276:333–340,1992Google Scholar
  26. 26.
    J. Scherk. An introduction to the theory of dual models and strings. Reviews of Modern Physics, 47:123–164,1975.Google Scholar
  27. 27.
    J. Serre. A Course in Arithmetics. Springer, New York, 1973.Google Scholar
  28. 28.
    P C. West. Physical States and String Symmetries. preprint HEP-TH/9411029, KCL-TH-94-19, 1994.Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  1. 1.IInd Institute for Theoretical PhysicsUniversity of HamburgHamburgGermany

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