2019
Том 71
№ 4

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

Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 8, pp 1199-1214.

Citation Example: Bodnarchuk Yu. V., Prokof’ev P. H. Locally nilpotent derivations and Nagata-type utomorphisms of a polynomial algebra // Ukr. Mat. Zh. - 2009. - 61, № 8. - pp. 1011-1024.

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