标题： 全局例外$\mathbb{Z}_2 \times \mathbb{Z}_2$-对称空间的实现 显示英文标题

标题： Realizations of globally exceptional $\mathbb{Z}_2 \times \mathbb{Z}_2$- symmetric spaces

摘要： 对由A.Kollross给出的例外$\mathbb{Z}_2 \times \mathbb{Z}_2$-对称空间$G/K$的分类，其中$G$是一个例外紧致李群或$S\!pin(8)$，并且此外$K$的结构被确定为李代数。 在本文中，我们具体给出了李代数$G$的一对交换的对合自同构（对合）$\tilde{\sigma}, \tilde{\tau}$，并确定了与李代数$\mathfrak{g}^\sigma \cap \mathfrak{g}^\tau$对应的群$G^{\sigma} \cap G^{\tau}$的结构，其中$G$是一个例外紧致李群。 由此，我们全局地实现了例外$\mathbb{Z}_2 \times \mathbb{Z}_2$-对称空间。 显示英文摘要

摘要： A classification is given of the exceptional $\mathbb{Z}_2 \times \mathbb{Z}_2$-symmetric spaces $G/K$ by A.Kollross, where $G$ is an exceptional compact Lie group or $S\!pin(8)$, and moreover the structure of $K$ is determined as Lie algebra. In the present article, we give a pair of commuting involutive automorphisms (involutions) $\tilde{\sigma}, \tilde{\tau}$ of $G$ concretely and determine the structure of group $G^{\sigma} \cap G^{\tau}$ corresponding to Lie algebra $\mathfrak{g}^\sigma \cap \mathfrak{g}^\tau$, where $G$ is an exceptional compact Lie group. Thereby, we realize exceptional $\mathbb{Z}_2 \times \mathbb{Z}_2$-symmetric spaces, globally.