完备群环中的共轭作用
The conjugation action in completed group rings
摘要：
设$k = \mathbb{F}_p$或$\mathbb{Z}_p$（或它们的有限扩张）。设$G$是一个$p$ -值群，并构成它的完备群代数$kG$ .通过分析$G$对自身的共轭作用，证明了两个结构结果。首先，我们证明了$kG$的所有保持$G$的内自同构都是由$G$的内自同构导出的.其次，对于$G$的闭子群$Γ$，对于由$Γ$的$G$ -中心化子诱导的理想$I$，我们计算了在$Γ$的共轭作用下$kG/I$的$Γ$ -固定环.
英文摘要：
Let $k = \mathbb{F}_p$ or $\mathbb{Z}_p$ (or finite extensions of these). Let $G$ be a $p$-valuable group, and form its completed group algebra $kG$. By analysing the conjugation action of $G$ on itself, we prove two structural results. Firstly, we show that all inner automorphisms of $kG$ that preserve $G$ are induced from inner automorphisms of $G$. Secondly, for a closed subgroup $Γ$ of $G$, we calculate the $Γ$-fixed ring of $kG/I$ under the conjugation action of $Γ$, for certain ideals $I$ induced from the $G$-centraliser of $Γ$.
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