Automorphisms of affine Veronese surfaces
Aitzhanova B. Umirbaev U.
1 March 2023World Scientific
International Journal of Algebra and Computation
2023#33Issue 2351 - 367 pp.
We prove that every derivation and every locally nilpotent derivation of the subalgebra K[xn,xn-1y,...,xyn-1,yn], where n ≥ 2, of the polynomial algebra K[x,y] in two variables over a field K of characteristic zero is induced by a derivation and a locally nilpotent derivation of K[x,y], respectively. Moreover, we prove that every automorphism of K[xn,xn-1y,...,xyn-1,yn] over an algebraically closed field K of characteristic zero is induced by an automorphism of K[x,y]. We also show that the group of automorphisms of K[xn,xn-1y,...,xyn-1,yn] admits an amalgamated free product structure.
Automorphism , derivation , e rational normal surface , free product , polynomial algebra
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Department of Mathematics, Wayne State University, Detroit, 48202, MI, United States
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Department of Mathematics
Institute of Mathematics and Mathematical Modeling
10 лет помогаем публиковать статьи Международный издатель
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