摘要翻译：
设$k$为特征域$p>0$。证明了Laurent多项式代数$L_n上微分算子环$\CD(L_n)$的保序自同构群$\aut_{ord}(\cd(L_n))$与群$\zp^n\rtimes\aut_k(L_n)$的斜直积同构，其中$\zp$是$p$-adic整数环。此外，显式地找到组$\aut_{ord}(\cd(L_n))$。类似地，$\aut_{ord}(\cdpn)\simeq\aut_k(P_n)$其中$P_n:=k[x_1,...,x_n]$是一个多项式代数。
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英文标题：
《The group of order preserving automorphisms of the ring of differential
  operators on Laurent polynomial algebra in prime characteristic》
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作者：
V. V. Bavula
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Rings and Algebras        环与代数
分类描述：Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups
非交换环与代数，非结合代数，泛代数与格论，线性代数，半群
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  Let $K$ be a field of characteristic $p>0$. It is proved that the group $\Aut_{ord}(\CD (L_n))$ of order preserving automorphisms of the ring $\CD (L_n)$ of differential operators on a Laurent polynomial algebra $L_n:= K[x_1^{\pm 1}, ..., x_n^{\pm 1}]$ is isomorphic to a skew direct product of groups $\Zp^n \rtimes \Aut_K(L_n)$ where $\Zp$ is the ring of $p$-adic integers. Moreover, the group $\Aut_{ord}(\CD (L_n))$ is found explicitly. Similarly, $\Aut_{ord}(\CDPn)\simeq \Aut_K(P_n)$ where $P_n: =K[x_1, ..., x_n]$ is a polynomial algebra.
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PDF链接：
https://arxiv.org/pdf/0806.1038