论文标题
杰出代数组的完全降低和亚组
Complete reducibility and subgroups of exceptional algebraic groups
论文作者
论文摘要
这篇调查文章有两个组成部分。第一部分对Serre的$ g $ complete降低性概念轻柔地介绍，其中$ g $是在代数封闭的字段上定义的连接还原的代数组。第二部分涉及该理论的后果，当$ g $简单的类型简单，特别是其在阐明$ g $的亚组结构中的作用。后一个主题的历史可以追溯到大约60年。直到今天，我们概述了已知的内容。我们还借此机会为文献提供了几个更正。
This survey article has two components. The first part gives a gentle introduction to Serre's notion of $G$-complete reducibility, where $G$ is a connected reductive algebraic group defined over an algebraically closed field. The second part concerns consequences of this theory when $G$ is simple of exceptional type, specifically its role in elucidating the subgroup structure of $G$. The latter subject has a history going back about sixty years. We give an overview of what is known, up to the present day. We also take the opportunity to offer several corrections to the literature.
