论文标题
八元国际电位罗森菲尔德空间的神奇方法
A magic approach to octonionic Rosenfeld spaces
论文作者
论文摘要
罗森菲尔德（Rosenfeld）在对谎言群体的几何形状的研究中，假设所有现实形式的特殊谎言群体与荷尔维茨代数（rank-2）张量的张量产物的异常形式之间存在严格的关系。不幸的是，罗森菲尔德（Rosenfeld）执行的程序并不严格，因为在代数的情况下，他一直使用的许多定理实际上并不是正确的，这些定理不是替代性和权力缔合性的。对于三十多年前，罗森菲尔德（Rosenfeld）在其等轴测组方面提出的所有平面的定义更为严格的方法可以在coset歧管理论中考虑，我们在这项工作中利用了这项工作，利用所有真实形式的魔术正方形，即在Hurwitz Normed Division Algebras及其分裂版本上进行的三个和两个命令。在我们的分析中，我们发现了7个伪里曼尼亚人对称的coset歧管，似乎在罗森菲尔德的框架内没有任何解释。我们对Rosenfeld线进行了类似的分析，并获得了许多伪里曼尼亚对称的coset，而这些伪用的coset没有任何解释。
In his study on the geometry of Lie groups, Rosenfeld postulated a strict relation between all real forms of exceptional Lie groups and the isometries of projective and hyperbolic spaces over the (rank-2) tensor product of Hurwitz algebras taken with appropriate conjugations. Unfortunately, the procedure carried out by Rosenfeld was not rigorous, since many of the theorems he had been using do not actually hold true in the case of algebras that are not alternative nor power-associative. A more rigorous approach to the definition of all the planes presented more than thirty years ago by Rosenfeld in terms of their isometry group, can be considered within the theory of coset manifolds, which we exploit in this work, by making use of all real forms of Magic Squares of order three and two over Hurwitz normed division algebras and their split versions. Within our analysis, we find 7 pseudo-Riemannian symmetric coset manifolds which seemingly cannot have any interpretation within Rosenfeld's framework. We carry out a similar analysis for Rosenfeld lines, obtaining that there are a number of pseudo-Riemannian symmetric cosets which do not have any interpretation à la Rosenfeld.
