紧例外李群$F_4, E_6$和$E_7$的两个对合自同构$σ, γ$的不动点子群
Fixed points subgroups by two involutive automorphisms $σ, γ$ of compact exceptional Lie groups $F_4, E_6$ and $E_7$
摘要：
对于单连通紧例外李群$G = F_4, E_6$和$E_7$，考虑两个对合$σ, γ$，并确定了$G$的子群$G^{σ,γ}$的群结构，这些子群是$G^σ$和$G^γ$的不动点子群的交$G^σ\cap G^γ$.动机如下。在[1]（见本文参考文献）中，我们确定了$(F_4)^{σ, σ'}, (E_6)^{σ, σ'}$和$(E_7)^{σ, σ'}$的群结构，在[2]（见本文参考文献）中，我们也确定了$(G_2)^{γ, γ'}, (F_4)^{γ, γ'}$和$(E_6)^{γ, γ'}$的群结构。因此，本文试图确定群$(F_4)^{σ, γ}, (E_6)^{σ, γ}$和$(E_7)^{σ, γ}$的类型。
英文摘要：
For simply connected compact exceptional Lie groups $G = F_4, E_6$ and $E_7$, we consider two involutions $σ, γ$ and determine the group structure of subgroups $G^{σ,γ}$ of $G$ which are the intersection $G^σ\cap G^γ$ of the fixed points subgroups of $G^σ$ and $G^γ$. The motivation is as follows. In [1](see the References of this paper), we determine the group structure of $(F_4)^{σ, σ'}, (E_6)^{σ, σ'}$ and $(E_7)^{σ, σ'}$, and in [2](see the References of this paper), we also determine the group structure of $(G_2)^{γ, γ'}, (F_4)^{γ, γ'}$ and $(E_6)^{γ, γ'}$. So, in this paper, we try to determine the type of groups $(F_4)^{σ, γ}, (E_6)^{σ, γ}$ and $(E_7)^{σ, γ}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
