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- W4386697852 abstract "In the paper, we study the isotropy groups of K[x] if D is a simple derivation. We first study the derivation of the form: D=∂x1+∑i=2n(aixi+bi)∂xi with ai,bi∈K[x1,…,xi−1] for all 2≤i≤n. We prove that Aut(K[x])D={id} if D is simple with degxi−1ai≥1 for all 2≤i≤n or ai∈K* for all 3≤i≤n or 0≤degxjbi≤degxjai for all 2≤j≤i−1,3≤i≤n. Thus, we conjecture that Aut(K[x])D={id} if D is simple with ∏i=2nai≠0,ai,bi∈K[x1,…,xi−1] for all 2≤i≤n. Then we prove that Aut(K[x])D={(x1,…,xn−1,xn+c)|c∈K} if D=(x1sx2+g)∂x1+x1s−1∂x2+g3∂x3+⋯+gn∂xn or D=(x1sx2t+c)∂x1+x1r∂x2+g3∂x3+⋯+gn∂xn with g∈K[x1],deg(g)≤s,g(0)≠0 and gi∈K[xi−1]K for all 3≤i≤n." @default.
- W4386697852 created "2023-09-14" @default.
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- W4386697852 date "2023-09-13" @default.
- W4386697852 modified "2023-10-18" @default.
- W4386697852 title "Simple derivations and the isotropy groups" @default.
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- W4386697852 doi "https://doi.org/10.1080/00927872.2023.2255896" @default.
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