论文标题
完整的降低性：塞雷主题的变化
Complete reducibility: Variations on a theme of Serre
论文作者
论文摘要
在本说明中，我们在$ g $ complete降低的区域中统一和扩展了各种概念，其中$ g $是一个还原的代数组。根据Serre和Bate-Martin-Röhrle的结果，可以将$ g $ complete降低的常见概念重新构架为一个小组在$ g $的身份组件的球形建筑中的属性。我们表明，该概念的其他变体，例如相对完全的可降低性和$σ$ - 完整的降低性，也可以看作是该建筑物理论定义的特殊情况，因此这些领域的许多结果都是更一般属性的特殊情况。
In this note, we unify and extend various concepts in the area of $G$-complete reducibility, where $G$ is a reductive algebraic group. By results of Serre and Bate--Martin--Röhrle, the usual notion of $G$-complete reducibility can be re-framed as a property of an action of a group on the spherical building of the identity component of $G$. We show that other variations of this notion, such as relative complete reducibility and $σ$-complete reducibility, can also be viewed as special cases of this building-theoretic definition, and hence a number of results from these areas are special cases of more general properties.
