Skip to main content
SpringerLink
Log in

Structure of groups of nonlinear automorphisms for (3,3) quadrics

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

We study the group of nonlinear automorphisms for (k, n) quadrics. We prove that this group is nilpotent and describe the multiplication law for this group in terms of the corresponding Lie algebra. For nonlinear automorphisms of (3,3) quadrics, explicit formulas are obtained.

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. B. V. Shabat,Introduction to Complex Analysis [in Russian], “Nauka”, Moscow (1985).

    Google Scholar 

  2. V. K. Beloshapka, “Holomorphic transformations of a quadric,”Mat. Sb. [Math. USSR-Sb.],182, No. 2, 203–219 (1991).

    MATH  Google Scholar 

  3. A. A. Kirillov,Elements of the Theory of Representations [in Russian], “Nauka”, Moscow (1978).

    Google Scholar 

  4. N. Jacobson,Lie Algebras, Interscience Publishers, New York-London (1962).

    Google Scholar 

  5. H. Poincaré, “Les fonctions analytiques de deux variables et la représentation conforme,”Rend. Circ. Math. Palermo, 185–220 (1907).

  6. V. V. Ezhov (Ezov) and G. Schmalz, “Holomorphic automorphisms of quadrics,”Math. Z.,216, 453–470 (1994).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University, USSR

    A. F. Arbatskii

Authors
  1. A. F. Arbatskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematicheskie Zametki, Vol. 59, No. 2, pp. 164–173, February, 1996.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arbatskii, A.F. Structure of groups of nonlinear automorphisms for (3,3) quadrics. Math Notes 59, 116–122 (1996). https://doi.org/10.1007/BF02310949

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02310949

Keywords

Search

Navigation