Skip to main content
SpringerLink
Log in

Periodic automorphisms of the free Lie algebra of rank 3

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We prove that each automorphism of finite order of the free Lie algebra of rank 3 over an algebraically closed field is conjugate to a linear automorphism if the field characteristic fails to divide the automorphism order.

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. Shestakov I. P. and Umirbaev U. U., “The tame and the wild automorphisms of polynomial rings in three variables,” J. Amer. Math. Soc., 17, No. 1, 197–227 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  2. Shestakov I. P. and Umirbaev U. U., “Poisson brackets and two-generated subalgebras of rings of polynomials,” J. Amer. Math. Soc., 17, No. 1, 181–196 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  3. Umirbaev U. U., “Defining relations of the tame automorphism group of polynomial algebras in three variables,” J. Reine Angew. Math. (Crelles Journal), No. 600, 203–235 (2006).

  4. Umirbaev U. U., “Defining relations for automorphism groups of free algebras,” J. Algebra, 314, No. 1, 209–225 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  5. Drensky V., “Fixed algebras of residually nilpotent Lie algebras,” Proc. Amer. Math. Soc., 120, No. 4, 1021–1028 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  6. Petrogradskiĭ V. M., “On invariants of the action of a finite group on a free Lie algebra,” Siberian Math. J., 41, No. 4, 763–770 (2000).

    Article  MathSciNet  Google Scholar 

  7. Cohn P. M., “The automorphism group of the free algebra of rank two,” Serdica Math. J., No. 28, 255–266 (2002).

  8. Bourbaki N., Lie Groups and Algebras. Free Lie Algebras and Lie Groups [Russian translation], Mir, Moscow (1976).

    Google Scholar 

  9. Cohn P. M., “Subalgebras of free associative algebras,” Proc. London Math. Soc., 56, 618–632 (1964).

    Article  Google Scholar 

  10. Serre J.-P., Trees, Springer-Verlag, Berlin, Heidelberg, and New York (1980).

    MATH  Google Scholar 

  11. Magnus W., Karrass A., and Solitar D., Combinatorial Group Theory [in Russian], Nauka, Moscow (1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Omsk State University, Omsk, Russia

    M. A. Shevelin

Authors
  1. M. A. Shevelin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. A. Shevelin.

Additional information

Original Russian Text Copyright © 2011 Shevelin M. A.

__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 3, pp. 690–700, May–June, 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shevelin, M.A. Periodic automorphisms of the free Lie algebra of rank 3. Sib Math J 52, 544–553 (2011). https://doi.org/10.1134/S0037446611030177

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446611030177

Keywords

Search

Navigation