关于Shamsuddin导子与迷向群
On Shamsuddin derivations and the isotropy groups
摘要：
本文对\cite{13}中的猜想给出了肯定的回答。我们证明了一个Shamsuddin导子$D$是简单的当且仅当$\operatorname{Aut}(K[x,y_1,\allowbreak\ldots,y_n])_D=\{id\}$.此外，我们还计算了$K[x,y_1,\ldots,y_r]$的Shamsuddin导子$d=\partial_x+\sum_{j=1}^r(a(x)y_j+b_j(x))\partial_j$的各向同性群.我们还证明了$d$是Mathieu-Zhao子空间当且仅当$a(x)\in K$.
英文摘要：
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 $a(x)\in K$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
