论文标题
由代数元素组成的仿射品种的自动形态群
Automorphism groups of affine varieties consisting of algebraic elements
论文作者
论文摘要
给定仿射代数$ x $，我们证明，如果自动形态元素的中性组件$ \ mathrm {aut}^\ circ（x）$由代数元素组成，那么它是嵌套的，即，是代数亚基的直接极限。这改善了我们的早期结果。为了证明这一点，我们获得以下事实。如果连接的Indgroup $ G $包含一个封闭的连接嵌套的Ind-Subgroup $ H \ subset G $，对于任何$ g \ in G $中的任何$ g $的$ g $的$ g $属于$ h $，则属于$ g =h。$。
Given an affine algebraic variety $X$, we prove that if the neutral component $\mathrm{Aut}^\circ(X)$ of the automorphism group consists of algebraic elements, then it is nested, i.e., is a direct limit of algebraic subgroups. This improves our earlier result. To prove it, we obtain the following fact. If a connected ind-group $G$ contains a closed connected nested ind-subgroup $H\subset G$, and for any $g\in G$ some positive power of $g$ belongs to $H$, then $G=H.$
