关于李群的实现$ G_{2,\boldmath\scriptstyle{H}},F_{4,\boldmath\scriptstyle{H}},E_{6,\boldmath\scriptstyle{H}},E_{7,\boldmath\scriptstyle{H}},E_{8,\boldmath\scriptstyle{H}} $，第二版
On realizations of the Lie groups $ G_{2,\boldmath\scriptstyle{H}},F_{4,\boldmath\scriptstyle{H}},E_{6,\boldmath\scriptstyle{H}},E_{7,\boldmath\scriptstyle{H}},E_{8,\boldmath\scriptstyle{H}} $, second edition
摘要：
为了定义例外紧李群$G_2,F_4,E_6,E_7,E_8$，我们通常使用Cayley代数$\mathfrak{C}$或它的复化$\mathfrak{C}^C$ .本文考虑用四元数域$\boldmath{H}$代替Cayley代数$\mathfrak{C}$来定义上述群，这些群记作上述群.我们的目标是确定这些群体的结构。我们称之为实现来决定群体的结构。
英文摘要：
In order to define the exceptional compact Lie groups $G_2,F_4,E_6,E_7,E_8$, we usually use the Cayley algebra $\mathfrak{C}$ or its complexification $\mathfrak{C}^C$. In the present article, we consider replacing the Cayley algebra $\mathfrak{C}$ with the field of quaternion numbers $\boldmath{H}$ in the definition of the groups above, and these groups are denoted as in title above. Our aim is to determine the structure of these groups. We call realization to determine the structure of the groups.
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