标题： 任意实代数群的分量群的计算 显示英文标题

标题： Computation of the component group of an arbitrary real algebraic group

摘要： 我们显式计算了实李群$G(\mathbb{R})$的连通分支群$\pi_0G(\mathbb{R})$，对于在实数域$\mathbb{R}$上定义的任意（不一定为线性的）连通代数群$G$。 特别是，结果表明$\pi_0G(\mathbb{R})$总是一个初等阿贝尔 2-群。 当$G$是一个线性代数群或阿贝尔簇时，结果最为清晰。 该计算基于代数群的结构结果和伽罗瓦上同调方法。 显示英文摘要

摘要： We compute explicitly the group of connected components $\pi_0G(\mathbb{R})$ of the real Lie group $G(\mathbb{R})$ for an arbitrary (not necessarily linear) connected algebraic group $G$ defined over the field $\mathbb{R}$ of real numbers. In particular, it turns out that $\pi_0G(\mathbb{R})$ is always an elementary Abelian 2-group. The result looks most transparent in the cases where $G$ is a linear algebraic group or an Abelian variety. The computation is based on structure results on algebraic groups and Galois cohomology methods.