论文标题
G2，F4和E6的八元平面和真实形式
Octonionic Planes and Real Forms of G2, F4 and E6
论文作者
论文摘要
在这项工作中，我们提出了一种有用的方法，可以通过使用Veronese矢量引入八世纪射射线和双曲线平面。然后，我们将重点放在它们与杰出的约旦代数的关系上，并表明Veronese矢量是代数的一部分元素。然后，我们研究了八元离子平面上的运动组，以恢复所有真实形式的G2，F4和E6组，并最终将所有八世纪和分裂的平面分类为对称空间。
In this work we present a useful way to introduce the octonionic projective and hyperbolic plane through the use of Veronese vectors. Then we focus on their relation with the exceptional Jordan algebra and show that the Veronese vectors are the rank-one elements of the algebra. We then study groups of motions over the octonionic plane recovering all real forms of G2, F4and E6 groups and finally give a classification of all octonionic and split-octonionic planes as symmetric spaces.
