Fano平面的入射几何与构造（分裂）八元数的Freudenthal不等式
Incidence geometry of the Fano plane and Freudenthal's ansatz for the construction of (split) octonions
摘要：
在这篇文章中，我们考虑结构上的Fano平面${\cal F}$允许一个推广弗赖登塔尔的建设规范和双线性乘法律的八维向量空间${\mathbb O_{\cal F}}$规范相关的${\cal F}$。我们首先确定的充要条件，这些结构的${\cal F}$的关联几何产生司复合代数，并分类相应的结构使用对数版本的乘法。然后，我们展示了如何这些结果可以用来推导类似的结果在分裂复合代数的情况下。
英文摘要：
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.
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