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arXiv 2107.09401math.RA
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Ore扩张$K[x][y; δ]$（零特征）的同构问题和自同构群

Isomorphism problems and groups of automorphisms for Ore extensions $K[x][y; δ]$ (zero characteristic)

V. V. Bavula

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11 pages
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摘要：

设$Ł(f) = K[x][y; f\frac{d}{dx} ]$是特征为零的域$K$上多项式代数$K[x]$的Ore扩张，其中$f\in K[x]$ .对于给定的多项式$f$，明确地描述了代数$Ł(f) $的自同构群。多项式情形$Ł(0) = K[x,y]$和Weyl代数$A_1= K[x][y; \frac{d}{dx} ]$的情形分别由Jung（1942）、van der Kulk（1953）和Dixlane（1968）完成。1997年，Alev和Dumas证明了代数$Ł(f)$和$Ł(g)$同构当且仅当对于某些$ł, α\in K\backslash \{ 0\}$和$β\in K$，$g(x) = łf(αx+β)$. 2015年，Benkart、Lopes和Ondrus给出了代数$Ł(f)$的自同构群集合的完整描述。在本文中，我们完成的图片，即{ \em给定}的多项式$f$，我们有明确的描述$Ł(f)$的自同构群。

英文摘要：

Let $Ł(f) = K[x][y; f\frac{d}{dx} ]$ be an Ore extension of a polynomial algebra $K[x]$ over a field $K$ of characteristic zero where $f\in K[x]$. For a given polynomial $f$, the automorphism group of the algebra $Ł(f) $ is explicitly described. The polynomial case $Ł(0) = K[x,y]$ and the case of the Weyl algebra $A_1= K[x][y; \frac{d}{dx} ]$ were done done by Jung (1942) and van der Kulk (1953), and Dixmier (1968), respectively. In 1997, Alev and Dumas proved that the algebras $Ł(f)$ and $Ł(g)$ are isomorphic iff $g(x) = łf(αx+β)$ for some $ł, α\in K\backslash \{ 0\}$ and $β\in K$. In 2015, Benkart, Lopes and Ondrus gave a complete description of the set of automorphism groups of algebras $Ł(f)$. In this paper we complete the picture, i.e. {\em given} the polynomial $f$ we have the explicit description of the automorphism group of $Ł(f)$.

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。

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