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Ukrainian Mathematical Journal

, Volume 61, Issue 8, pp 1199–1214 | Cite as

Locally nilpotent derivations and Nagata-type utomorphisms of a polynomial algebra

  • Yu. V. Bodnarchuk
  • P. H. Prokof’ev
Article
  • 47 Downloads

We study locally nilpotent derivations belonging to a Lie algebra sa n of a special affine Cremona group in connection with the root decompositions of sa n relative to the maximum standard torus. It is proved that all root locally nilpotent derivations are elementary. As a continuation of this research, we describe two- and three-root derivations. By using the results obtained by Shestakov and Umirbaev, it is shown that the exponents of almost all obtained three-root derivations are wild automorphisms of a polynomial algebra in three variables.

Keywords

Polynomial Algebra Root Decomposition Root Space Elementary Derivation Jacobian Conjecture 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  • Yu. V. Bodnarchuk
    • 1
  • P. H. Prokof’ev
    • 1
  1. 1.“Kyevo-Mohylyans’ka Akademiya” UniversityKyivUkraine

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