Skip to main content
SpringerLink
Log in

Complete commutative sets of polynomials for solvable Lie algebras of dimension six and nilpotent Lie algebras of dimension seven

  • Published:
Moscow University Mathematics Bulletin Aims and scope

Abstract

A complete commutative set of polynomials is constructed using Sadetov’s method on the coalgebra of each real 6-dimensional solvable non-nilpotent Lie algebra and of each real 7-dimensional nilpotent Lie algebra.

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. S. Mishchenko and A. T. Fomenko, “Euler Equations on Finite-Dimensional Lie Groups,” Izvestiya Akad. Nauk SSSR 12(2), 396 (1978) [Math. of the USSR-Izvestiya 12 (2), 371 (1978)].

    Google Scholar 

  2. S. T. Sadetov, “Proof of Mishchenko-Fomenko Conjecture,” Doklady Russ. Akad. Nauk 397(6), 751 (2004) [Doklady Math. 70 (1), 635 (2004)].

    MathSciNet  Google Scholar 

  3. A. V. Bolsinov, “Complete Involutive Sets of Polynomials on Poisson Algebras: the Proof of Mishchenko-Fomenko Conjecture,” Trudy Semin. Vect. Tenz. Analiz. 26, 87 (2005).

    MATH  Google Scholar 

  4. G. M. Mubarakzyanov, “On Solvable Lie Algebras,” Izvestiya Vyssh. Uchebn. Zaved. Matem., No. 1, 114 (1963).

  5. E. N. Safiullina, “Classification of Nilpotent Lie Algebras of Order 7,” in Candidates Works, Math., Mech., Phys. (Kazan Univ., Kazan, 1964), pp. 103–105 [in Russian].

    Google Scholar 

  6. A. A. Korotkevich, “Integrable Hamiltonian Systems on Low-Dimensional Lie Algebras,” Matem. Sborn. 200(12), 3 (2009) [Sbornik: Math. 200 (12), 1731 (2009)].

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    A. A. Korotkevich

Authors
  1. A. A. Korotkevich
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.A. Korotkevich, 2011, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2011, Vol. 66, No. 5, pp. 21–26.

About this article

Cite this article

Korotkevich, A.A. Complete commutative sets of polynomials for solvable Lie algebras of dimension six and nilpotent Lie algebras of dimension seven. Moscow Univ. Math. Bull. 66, 204–209 (2011). https://doi.org/10.3103/S0027132211050044

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0027132211050044

Keywords

Search

Navigation