Skip to main content
SpringerLink
Log in

Automorphisms Group of an Invariant Subalgebra of a Reductive Lie Algebra

  • Published:
Acta Applicandae Mathematica Aims and scope Submit manuscript

Abstract

We prove that any automorphism of an invariant subalgebra of a reductive Lie algebra over a field of zero characteristic is a standard automorphism.

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. Humphreys, J.: Introduction to Lie Algebras, Springer-Verlag, New York, 1972.

    Google Scholar 

  2. Jacobson, N.: Lie Algebras, Int. Publ., New York, 1958.

    Google Scholar 

  3. Myasnikov, A. G. and Remeslennikov, V. N.: Definability of the set of Mal’sev bases and elementary theories of finite-dimensional algebras, Sibirsk. Mat. Zh. 24(2) (1983), 97–113.

    Google Scholar 

  4. Ponomarev, K. N.: Fields of representatives of commutative local rings and maximal scalar fields of finite-dimensional algebras, Algebra and Logic 37(6) (1998), 667–686.

    Google Scholar 

  5. Ponomarev, K. N.: Invariant Lie algebras and Lie algebras with small centroid, Algebra and Logic 40(6) (2001).

  6. Ponomarev, K. N. and Firat, A.: Groups of automorphisms of Chevalley algebras, Comm. in Algebra 29(9) (2001), 4139–4155.

    Google Scholar 

  7. Ponomarev, K. N.: Groups of automorphisms of tensor completion of Lie algebras, In: International Conference in Algebra and its Applications, Krasnoyarsk, 2002, p. 145.

  8. Segal, D.: On the automorphism group of certain Lie algebras, Math. Proc. Cambridge Philos. Soc. 106 (1989), 67–76.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Novosibirsk State Technical University, Novosibirsk, Russia

    K. N. Ponomarjev

Authors
  1. K. N. Ponomarjev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. N. Ponomarjev.

Additional information

Mathematics Subject Classifications (2000)

17B20, 17B40.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ponomarjev, K.N. Automorphisms Group of an Invariant Subalgebra of a Reductive Lie Algebra. Acta Appl Math 85, 251–255 (2005). https://doi.org/10.1007/s10440-004-5626-0

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10440-004-5626-0

Keywords

Search

Navigation