关于复数李群 $ (F_{4,R})^C, (E_{6,R})^C, (E_{7,R})^C ,(E_{8,R})^C$ 和那些紧凑实数形式 $F_{4,R},E_{6,R},E_{7,R},E_{8,R}$ 的实数化

Toshikazu Miyashita
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引用次数: 0

摘要

为了定义复例外李群 ${F_4}^C, {E_6}^C,{E_7}^C, {E_8}^C $ 以及这些紧凑实形式 $F_4,E_6,E_7,E_8$,我们通常使用 Cayley 代数 $\mathfrak{C} $。在本文中,我们考虑在上述群的定义中用实数域$\mathbb R$来代替 Cayley 代数$\mathfrak{C}$,这些群的名称如上。我们的目的是确定这些群的结构。我们称实现为确定群的结构。
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On realizations of the complex Lie groups $ (F_{4,R})^C, (E_{6,R})^C, (E_{7,R})^C ,(E_{8,R})^C$ and those compact real forms $F_{4,R},E_{6,R},E_{7,R},E_{8,R}$
In order to define the complex exceptional Lie groups $ {F_4}^C, {E_6}^C, {E_7}^C, {E_8}^C $ and these compact real forms $ F_4,E_6,E_7,E_8 $, we usually use the Cayley algebra $ \mathfrak{C} $. In the present article, we consider replacing the Cayley algebra $ \mathfrak{C} $ with the field of real numbers $\mathbb R$ 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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