Skip to main content
SpringerLink
Log in

Kronecker indices of Lie algebras and invariants degrees estimate

  • Published:
Moscow University Mathematics Bulletin Aims and scope

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.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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)].

    MATH  MathSciNet  Google Scholar 

  2. A. V. Bolsinov, and A. A. Oshemkov, “Bi-Hamiltonian Structures and Singularities of Integrable Systems,” Regular and Chaotic Dynamics 14, 431 (2009).

    Article  MathSciNet  Google Scholar 

  3. I. Zakharevich, “Kronecker Webs, Bihamiltonian Structures, and the Method of Argument Translation,” Transformation Groups 6(3), 267 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  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. 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)].

    MathSciNet  Google Scholar 

  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. R. C. Thompson, “Pencils of Complex and Real Symmetric and Skew Matrices,” Linear Algebra and Appl. 147, 323 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    A. S. Vorontsov

Authors
  1. A. S. Vorontsov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.S. Vorontsov, 2011, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2011, Vol. 66, No. 1, pp. 26–30.

About this article

Cite this article

Vorontsov, A.S. Kronecker indices of Lie algebras and invariants degrees estimate. Moscow Univ. Math. Bull. 66, 25–29 (2011). https://doi.org/10.3103/S0027132211010050

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0027132211010050

Keywords

Search

Navigation