论文标题
在shamsuddin衍生和各向同性基团上
On Shamsuddin derivations and the isotropy groups
论文作者
论文摘要
在论文中，我们在\ cite {13}中对猜想做出了肯定的答案。我们证明，仅当$ \ operatatorName {aut}（k [x，y_1，\ allay break \ ldots，y_n]）_ d = \ {id {id \} $时，仅当$ \ operataTorname {aut}（k [x，y_1，\ lassionbreak \ ldots，y_1，\ ldots）时，我们证明了shamsuddin $ d $很简单。此外，我们计算了shamsuddin衍生的各向同性组$ d = \ partial_x+\ sum_ {j = 1}^r（a（x）y_j+b_j（x））\ partial_j $ of $ k [x，y_1，y_1，y_1，\ ldots，y_r，y_r，y_r] $。我们还证明$ d $是Mathieu-Zhao子空间，并且仅当$ a（x）\ in K $中。
In the paper, we give an affirmative answer to the conjecture in \cite{13}. We prove that a Shamsuddin derivation $D$ is simple if and only if $\operatorname{Aut}(K[x,y_1,\allowbreak\ldots,y_n])_D=\{id\}$. In addition, we calculate the isotropy groups of the Shamsuddin derivations $d=\partial_x+\sum_{j=1}^r(a(x)y_j+b_j(x))\partial_j$ of $K[x,y_1,\ldots,y_r]$. We also prove that $d$ is a Mathieu-Zhao subspace if and only if $a(x)\in K$.
