Locally nilpotent derivations and Nagata-type utomorphisms of a polynomial algebra
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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.
KeywordsPolynomial Algebra Root Decomposition Root Space Elementary Derivation Jacobian Conjecture
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