Advertisement

Quantum groups

  • L. D. Faddeev
Article

Abstract

An elementary introduction to the notions of the quantum Lie Groups and quantum Lie algebras is given. The approach is based on the fundamental commutation relations which appeared first in the quantum inverse scattering method.

Keywords

Hopf Algebra Quantum Group Cartan Subgroup Quantum Inverse Main Relation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. Sklyanin, L. Takhtajan, L. Faddeev, TMF40, 2 (1979). pp. 194–220 (in Russian)Google Scholar
  2. 2.
    L. Takhtajan, L. Faddeev, UMN34, 5 (1979), 16–63. (in Russian) Russian Math. Surveys34, 5 (1979), 11–61.Google Scholar
  3. 3.
    L. Faddeev, L. Takhtajan, “Hamiltonian Methods in the Theory of Solitons,” Springer-Verlag, 1987.Google Scholar
  4. 4.
    L. Faddeev, “Les Houches Lectures 1982,” Elsevier, Amsterdam, 1984.Google Scholar
  5. 5.
    P. Kulish, N. Reshetikhin,Zap. Nauch. Semin. LOMI. (in Russian) J. Soviet Math.23 (1983), 2435–2441.Google Scholar
  6. 6.
    E. Sklyanin, Funct. Anal. Appl.16 (1982), 27–34;17 (1983), 34–48.MathSciNetGoogle Scholar
  7. 7.
    V. Drinfeld, Dokl. Akad. Nauk USSR283 (1985), 1060–1064.MathSciNetGoogle Scholar
  8. 8.
    V. Drinfeld, Berkeley, Proceed. Inter. Congr. Math.1 (1986), 798–820.Google Scholar
  9. 9.
    M. Jimbo, Commun. Math. Phys.102, 4 (1986), 537–548.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    —, Lett. Math. Phys.10, 1 (1985), 63–69.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    V. Bazhanov, Commun. Math. Phys.113 (1987), 471–503.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    L. Faddeev, N. Reshetikhin, L. Takhtajan, LOMI preprintE-14-87 (1987).Google Scholar
  13. 13.
    L. Faddeev, “Algebra and Analysis,” 1989.Google Scholar
  14. 14.
    Yu. Manin, PreprintCRM-156 (1988). MontrealGoogle Scholar
  15. 15.
    N. Reshetikhin, LOMI preprintE-4-87 (1988); LOMI preprintE-17-87 (1988).Google Scholar
  16. 16.
    A. Kohno, Ann. l'Inst. Fourier37 (1987). fasc. 4Google Scholar
  17. 17.
    G. Moore, N. Seiberg, IAS-preprint8-30-88 (1988).Google Scholar
  18. 18.
    A. Kirillov, Zap. Nauch. Semin. LOMI134 (1984), 169–189. (in Russian)MathSciNetGoogle Scholar
  19. 19.
    A. Kirillov, N. Reshetikhin, Zap. Nauch. Semin. LOMI155 (1986), 65–115. (in Russian)Google Scholar

Copyright information

© Sociedade Brasileira de Matemática 1989

Authors and Affiliations

  • L. D. Faddeev
    • 1
  1. 1.Steklov Mathematical InstituteLeningrad

Personalised recommendations