Том 71
№ 7

All Issues

Prokof’ev P. H.

Articles: 1
Article (Ukrainian)

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

Bodnarchuk Yu. V., Prokof’ev P. H.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 8. - pp. 1011-1024

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.