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Theoretical and Mathematical Physics

, Volume 120, Issue 2, pp 1019–1025 | Cite as

Generalized Heisenberg equations on ℤ-graded Lie algebrasLie algebras

  • I. Z. Golubchik
  • V. V. Sokolov
Article

Abstract

We study the integrable systems of the Heisenberg equation type that correspond to different decompositions of ℤ-graded Lie algebras into a direct sum of two subalgebras. We discover new non-Abelian generalizations of some known integrable models.

Keywords

Current Algebra Semisimple Element Heisenberg Equation Jordan Pair Jordan System 
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References

  1. 1.
    O. I. Mokhov and E. V. Ferapontov,Funct. Anal. Appl.,28, 123–125 (1994).CrossRefMathSciNetGoogle Scholar
  2. 2.
    S. I. Svinolupov and V. V. Sokolov,Theor. Math. Phys.,108, 1160–1163 (1996).zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    I. Z. Golubchik and V. V. Sokolov,Theor. Math. Phys.,112, 1097–1103 (1997).zbMATHMathSciNetGoogle Scholar
  4. 4.
    L. A. Takhtadzhyan and L. D. Faddeev,The Hamiltonian Methods in the Theory of Solitons [in Russian], Nauka, Moscow (1986); English transl., L. D. Faddeev and L. A. Takhtajan, Berlin, Springer (1987).zbMATHGoogle Scholar
  5. 5.
    V. G. Drinfeld and V. V. Sokolov, “Lie algebras and Korteweg-de Vries-type equations,” in:Results in Science and Technology—Contemporary Problems in Mathematics: Fundamental Directions [in Russian] (R. V. Gamkrelidze, ed.) Vol. 24, VINITI, Moscow (1984), pp. 81–180.Google Scholar
  6. 6.
    S. I. Svinolupov and V. V. Sokolov,Theor. Math. Phys.,100, 959–962 (1994).zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    O. V. Mel'nikov, V. N. Remeslennikov, V. A. Roman'kov, L. A. Skornyakov, and I. P. Shestakov,General Algebra [in Russian], Vol. 1, Nauka, Moscow (1990).zbMATHGoogle Scholar
  8. 8.
    I. T. Habibullin, V. V. Sokolov, and R. I. Yamilov, “Multi-component integrable systems and nonassociative structures,” in:Nonlinear Physics: Theory and Experiment (E. Alfinito et al., eds.), World Scientific, Singapore (1996), pp. 139–168.Google Scholar
  9. 9.
    V. Ostapenko,C. R. Acad. Sci. Paris,315 (Ser. I), 669–673 (1992).zbMATHMathSciNetGoogle Scholar
  10. 10.
    A. Stolin,Math. Scand.,69, 57–80 (1991).MathSciNetGoogle Scholar
  11. 11.
    A. A. Belavin and V. G. Drinfeld,Funct. Anal. Appl.,16, 159–180 (1982).CrossRefMathSciNetGoogle Scholar
  12. 12.
    M. A. Semenov-Tyan-Shanskii,Funct. Anal. Appl.,17, 259–272 (1983).CrossRefMathSciNetGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • I. Z. Golubchik
    • 1
  • V. V. Sokolov
    • 2
  1. 1.Ufa Pedagogical InstituteUfaRussia
  2. 2.Landau Institute for Theoretical PhysicsRASChernogolovkaRussia

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