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- W4384755712 abstract "The Veronese subalgebra $A_0$ of degree $dgeq 2$ of the polynomial algebra $A=K[x_1,x_2,ldots,x_n]$ over a field $K$ in the variables $x_1,x_2,ldots,x_n$ is the subalgebra of $A$ generated by all monomials of degree $d$ and the Veronese subalgebra $P_0$ of degree $dgeq 2$ of the free Poisson algebra $P=Plangle x_1,x_2,ldots,x_nrangle$ is the subalgebra spanned by all homogeneous elements of degree $kd$, where $kgeq 0$. If $ngeq 2$ then every derivation and every locally nilpotent derivation of $A_0$ and $P_0$ 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 $A_0$ and $P_0$ over a field $K$ closed with respect to taking all $d$-roots of elements is induced by an automorphism of $A$ and $P$, respectively." @default.
- W4384755712 created "2023-07-20" @default.
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- W4384755712 date "2023-07-15" @default.
- W4384755712 modified "2023-10-06" @default.
- W4384755712 title "Automorphisms of Veronese subalgebras of polynomial algebras and free Poisson algebras" @default.
- W4384755712 doi "https://doi.org/10.48550/arxiv.2307.07823" @default.
- W4384755712 hasPublicationYear "2023" @default.
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