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.
How to Cite
Bodnarchuk, Y. V., and P. H. Prokof’ev. “Locally Nilpotent Derivations and Nagata-Type Utomorphisms of a Polynomial Algebra”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, no. 8, Aug. 2009, pp. 1011-24, https://umj.imath.kiev.ua/index.php/umj/article/view/3077.
Research articles