Automorphisms of Veronese subalgebras of polynomial algebras and free Poisson algebras
Aitzhanova B. Makar-Limanov L. Umirbaev U.
1 March 2025World Scientific
Journal of Algebra and its Applications
2025#24Issue 3
The Veronese subalgebra A0 of degree d ≥ 2 of the polynomial algebra A = K[x1, x2, . . ., xn] over a field K in the variables x1, x2, . . ., xn is the subalgebra of A generated by all monomials of degree d and the Veronese subalgebra P0 of degree d ≥ 2 of the free Poisson algebra P = P〈x1, x2, . . ., xn〉 is the subalgebra spanned by all homogeneous elements of degree kd, where k ≥ 0. If n ≥ 2 then every derivation and every locally nilpotent derivation of A0 and P0 over a field K of characteristic zero is induced by a derivation and a locally nilpotent derivation of A and P, respectively. Moreover, we prove that every automorphism of A0 and P0 over a field K closed with respect to taking all d-roots of elements is induced by an automorphism of A and P, respectively.
Automorphism , derivation , free Poisson algebra , polynomial algebra
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Department of Mathematics Wayne State University, Detroit, 48202, MI, United States
Faculty of Mathematics and Computer Science, Weizmann Institute of Science, Rehovot, 7610001, Israel
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Department of Mathematics Wayne State University
Faculty of Mathematics and Computer Science
Institute of Mathematics and Mathematical Modeling
10 лет помогаем публиковать статьи Международный издатель
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