论文标题
Fano飞机和Freudenthal的Ansatz的发生率几何形状用于构建（分裂）八元
Incidence geometry of the Fano plane and Freudenthal's ansatz for the construction of (split) octonions
论文作者
论文摘要
在本文中，我们考虑了Fano平面上的结构$ {\ cal f} $，该结构允许对五维矢量空间$ {\ mathbb o _ {\ cal f}} $ canony canonaly canony can $ {\ cal f} $ contector $ {\ cal f} $ contector $ {\ mathbb o _ {\ mathbb o _ {\ mathbb o _ {\ mathbb o _ {\ mathbb o _ {\ mathbb o _ {\ cal f} $。我们首先根据$ {\ cal f} $的发生率几何形状确定必要和充分的条件，以使这些结构产生分裂组成代数，并使用乘法的对数版本对相应的结构进行分类。然后，我们展示如何使用这些结果来推断分裂组成代数案例中的类似结果。
In this article we consider structures on a Fano plane ${\cal F}$ which allow a generalisation of Freudenthal's construction of a norm and a bilinear multiplication law on an eight-dimensional vector space ${\mathbb O_{\cal F}}$ canonically associated to ${\cal F}$. We first determine necessary and sufficient conditions in terms of the incidence geometry of ${\cal F}$ for these structures to give rise to division composition algebras, and classify the corresponding structures using a logarithmic version of the multiplication. We then show how these results can be used to deduce analogous results in the split composition algebra case.
