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

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.


Polynomial Algebra Root Decomposition Root Space Elementary Derivation Jacobian Conjecture 
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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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