Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Quantization of the Gel'fand—Dikii brackets

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

Literature Cited

  1. 1.

    I. M. Gel'fand and L. A. Dikii, "Fractional powers of operators, and Hamiltonian systems," Funkts. Anal. Prilozhen.,10, No. 4, 13–29 (1976).

  2. 2.

    I. M. Gel'fand and L. A. Dikii, "The resolvent and Hamiltonian systems," Funkts. Anal. Prilozhen.,11, No. 2, 11–27 (1977).

  3. 3.

    V. G. Drinfel'd and V. V. Sokolov, "Lie algebras and equations of Korteweg—de Vries type," Itogi Nauki i Tekhniki, Sovrem. Probl. Mat.,24, 81–180 (1984).

  4. 4.

    S. L. Luk'yanov and V. A. Fateev, "Conformally invariant models of two-dimensional quantum field theory with Zn-symmetry," Zh. Éksp. Teor. Fiz.,94, No. 3, 23–37 (1988).

  5. 5.

    A. B. Zamolodchikov, "Infinite extra symmetries in two-dimensional conformal quantum field theory," Teor. Mat. Fiz.,65, No. 3, 347–359 (1985).

  6. 6.

    A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, "Infinite conformal symmetry in two-dimensional quantum field theory," Nucl. Phys.,241B, No. 2, 333–380 (1984).

  7. 7.

    N. N. Bogolyubov (Bogoliubov) and D. V. Shirkov, Introduction to the Theory of Quantized Fields (3rd ed.), Wiley, New York (1980).

  8. 8.

    L. D. Faddeev and L. A. Takhtadzhyan (L. A. Takhtajan), Hamiltonian Methods in the Theory of Solitons, Springer, Berlin (1987).

  9. 9.

    T. G. Khovanova, "Gelfand-Dikii Lie algebras and the Virasoro algebra," Funkts. Anal. Prilozhen.,20, No. 4, 89–90 (1986).

  10. 10.

    V. A. Fateev and A. B. Zamolodchikov, "Conformal quantum field theory models in two dimensions having Z3 symmetry," Nuclear Phys. B,280, 644–660 (1987).

  11. 11.

    B. L. Feigin and D. B. Fuks, "Skew-symmetric invariant differential operators on the line and Verma modules over the Virasoro algebra," Funkts. Anal. Prilozhen.,16, No. 2, 47–63 (1982).

Download references

Additional information

L. D. Landau Institute of Theoretical Physics. Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 22, No. 4, pp. 1–10, October–December, 1988.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Luk'yanov, S.L. Quantization of the Gel'fand—Dikii brackets. Funct Anal Its Appl 22, 255–262 (1988).

Download citation


  • Functional Analysis