例外群的对称空间
Symmetric Spaces of Exceptional Groups
摘要：
讨论了12个具有例外李群的对称空间存在的原因问题。分别为$G_2$和$F_4$的1+2例病例很容易从这些基团的八元离子性质解释。$E_{6,7,8}$级数的4+3+2情形需要弗赖登塔尔幻方，而对于分裂情形，则需要求助于$5, 4$和3维时空中的超引力链。
英文摘要：
We adress the problem of the reasons for the existence of 12 symmetric spaces with the exceptional Lie groups. The 1+2 cases for $G_2$ and $F_4$ respectively are easily explained from the octonionic nature of these groups. The 4+3+2 cases on the $E_{6,7,8}$ series require the magic square of Freudenthal and, for the split case, an appeal to the supergravity chain in $5, 4$ and 3 spacetime dimensions.
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。
