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

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Ukrainian Mathematical Journal Aims and scope

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.

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Authors and Affiliations

  1. “Kyevo-Mohylyans’ka Akademiya” University, Kyiv, Ukraine

    Yu. V. Bodnarchuk & P. H. Prokof’ev

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  1. Yu. V. Bodnarchuk
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  2. P. H. Prokof’ev
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 8, pp. 1011–1024, August, 2009.

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Bodnarchuk, Y.V., Prokof’ev, P.H. Locally nilpotent derivations and Nagata-type utomorphisms of a polynomial algebra. Ukr Math J 61, 1199–1214 (2009). https://doi.org/10.1007/s11253-010-0271-4

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  • DOI: https://doi.org/10.1007/s11253-010-0271-4

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