论文标题
线性代数群中的扭曲偶联性
Twisted conjugacy in linear algebraic groups
论文作者
论文摘要
让$ k $成为代数封闭的字段，$ g $是$ k $的线性代数组，而$ k $和$φ\ in Aut（g）$，$ g $的所有代数集团自动形态的组中。如果$ y =gxφ（g）（g）^{ - 1} $，则两个元素$ x，y $ $ $ g $的共轭为$φ$ -twisted共轭。在本文中，我们证明，对于连接的不可解决的线性代数组$ g $ of $ k $，其$φ$ twist的共轭类的数量对于aut（g）$中的每个$φ\ a都无限。
Let $k$ be an algebraically closed field, $G$ a linear algebraic group over $k$ and $φ\in Aut(G)$, the group of all algebraic group automorphisms of $G$. Two elements $x, y$ of $G$ are said to be $φ$-twisted conjugate if $y=gxφ(g)^{-1}$ for some $g\in G$. In this paper we prove that for a connected non-solvable linear algebraic group $G$ over $k$, the number of its $φ$-twisted conjugacy classes is infinite for every $φ\in Aut(G)$.
