Skip to main content
Log in

Solutions of the classical Yang - Baxter equation for simple Lie algebras

  • Published:
Functional Analysis and Its Applications Aims and scope

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. A. A. Belavin, "Discrete groups and integrability of quantum systems," Funkts. Anal.,14, No. 4, 18–26 (1980).

    Google Scholar 

  2. A. V. Zhiber and A. B. Shabat, "Klein—Gordon equations with nontrivial group," Dokl. Akad. Nauk SSSR,247, No. 5, 1103–1107 (1979).

    Google Scholar 

  3. V. G. Kats, "Automorphisms of finite order of semisimple Lie algebras," Funkts. Anal. Anal.,3, No. 3, 94–96 (1969).

    Google Scholar 

  4. V. G. Kats, "Simple irreducible graded Lie algebras of finite height," Izv. Akad. Nauk SSSR, Ser. Mat.,32, No. 6, 1323–1367 (1968).

    Google Scholar 

  5. P. P. Kulish and E. K. Sklyanin, "Solutions of the Yang—Baxter equation," in: Differential Geometry of Lie Groups and Mechanics [in Russian], Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,95, 129–160 (1980).

    Google Scholar 

  6. A. N. Leznov, M. V. Savel'ev, and V. G. Smirnov, "Theory of representations of groups and integration of nonlinear dynamical systems," Preprint IFVE, 80-51, Serpukhov: IFVE (1980).

    Google Scholar 

  7. I. G. MacDonald, "Affine systems of roots and the Dedekindŋ-function," Matematika,16, No. 4, 3–49 (1972).

    Google Scholar 

  8. J.-P. Serre, Lie Algebras and Lie Groups, W. A. Benjamin (1965).

  9. I. V. Cherednik, "Method of construction of factorized S-matrices in elementary functions," Teor. Mat. Fiz.,43, No. 1, 117–119 (1980).

    Google Scholar 

  10. O. I. Bogoyavlensky, "On perturbations of the periodic Toda lattice," Commun. Math. Phys.,51, 201–209 (1976).

    Google Scholar 

  11. V. G. Kac, "Infinite-dimensional algebras, Dedekind'sŋ-function, classical Möbius function and the very strange formula," Adv. Math.,30, No. 2, 85–136 (1978).

    Google Scholar 

  12. A. V. Michailov, M. A. Olshanetsky, and A. M. Perelomov, Preprint ITEP-64, Moscow: ITEP (1980).

    Google Scholar 

  13. S. A. Bulgadaev, "Two-dimensional integrable field theories connected with simple Lie algebras," P. L., 96B, 151–153 (1980).

    Google Scholar 

  14. A. I. Ooms, "On Lie algebras having a primitive universal enveloping algebra," J. Algebra,32, No. 3, 488–500 (1975).

    Google Scholar 

  15. A. I. Ooms, "On Lie algebras with primitive envelopes — Supplements," Proc. Am. Math. Soc.,58, 67–72 (1976).

    Google Scholar 

  16. A. I. Ooms, "On Frobenius Lie algebras," Commun. Algebra, 8(1), 13–52 (1980).

    Google Scholar 

  17. A. Weil, Varietes Abeliennes et Courbes Algebriques, Hermann, Paris (1948).

    Google Scholar 

  18. A. Weil, "On algebraic groups of transformations," Am. J. Math.,77, 355–391 (1955).

    Google Scholar 

Download references

Authors

Additional information

L. D. Landau Institute of Theoretical Physics, Academy of Sciences of the USSR. Physicotechnical Institute of Low Temperatures, Academy of Sciences of the Ukrainian SSR. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 16, No. 3, pp. 1–29, July–September, 1982.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Belavin, A.A., Drinfel'd, V.G. Solutions of the classical Yang - Baxter equation for simple Lie algebras. Funct Anal Its Appl 16, 159–180 (1982). https://doi.org/10.1007/BF01081585

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01081585

Keywords

Navigation