Advertisement

Kronecker indices of Lie algebras and invariants degrees estimate

  • A. S. Vorontsov
Article

Abstract

The concept of Kronecker indices of a Lie algebra as integer characteristics naturally connected to its structure tensor is introduced. A lower bound for the degrees of polynomial invariants of the co-adjoint action in terms of Kronecker indices is proved.

Keywords

Canonical Form Polynomial Invariant Kronecker Index Compatible Poisson Bracket Integer Characteristic 
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.

References

  1. 1.
    A. V. Bolsinov, “Compatible Poisson Brackets on Lie Algebras and Completeness of Families of Functions in Fnvolution,” Izv. Akad. Nauk SSSR, Ser. Matem. 55(1), 68 (1991). [Mathematics of the USSR, Izvestiya 38 (1), 69 (1992)].zbMATHMathSciNetGoogle Scholar
  2. 2.
    A. V. Bolsinov, and A. A. Oshemkov, “Bi-Hamiltonian Structures and Singularities of Integrable Systems,” Regular and Chaotic Dynamics 14, 431 (2009).CrossRefMathSciNetGoogle Scholar
  3. 3.
    I. Zakharevich, “Kronecker Webs, Bihamiltonian Structures, and the Method of Argument Translation,” Transformation Groups 6(3), 267 (2001).CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    A. S. Mishchenko and A. T. Fomenko, “Generalized Liouville Method of Integration of Hamiltonian Systems,” Funkts Anal. Prilozh. 12(2), 49 (1978) [Funct. Anal. and Its Appl. 12 (2), 113 (1978)].Google Scholar
  5. 5.
    V. V. Trofimov and A. T. Fomenko, “Liouville Integrability of Hamiltonian Systems on Lie Algebras,” Uspekhi Matem. Nauk 39(2), 3 (1984) [Russian Math. Surveys 39 (2), 1 (1984)].MathSciNetGoogle Scholar
  6. 6.
    A. T. Fomenko, “Algebraic Properties of Some Integrable Hamiltonian Systems,” in Lect. Notes Math. (Springer, Berlin 1984), Vol. 1060, pp. 246–257.Google Scholar
  7. 7.
    R. C. Thompson, “Pencils of Complex and Real Symmetric and Skew Matrices,” Linear Algebra and Appl. 147, 323 (1991).CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    A. S. Mishchenko and A. T. Fomenko, “Integrability of Euler Equations on Semisimple Lie Algebras,” in Proc. Workshop in Vector and Tensor Analysis (Moscow State Univ, Moscow, 1979), Vol. 19, pp. 3–94.Google Scholar

Copyright information

© Allerton Press, Inc. 2011

Authors and Affiliations

  • A. S. Vorontsov
    • 1
  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityLeninskie Gory, MoscowRussia

Personalised recommendations