论文标题
与特殊的正交表示与特殊谎言超级级别相关的特殊正交表示的几何特性
Geometric properties of special orthogonal representations associated to exceptional Lie superalgebras
论文作者
论文摘要
从一个特征而不是两个或三个字段的$ k $上的八元代数。 $ \ mathfrak {so}（{\ rm im}（\ mathbb {o}））$是特殊的正交表示。它们具有与二进制立方体相似的特殊几何属性，我们表明这些表示形式及其Mathews身份的协变量与Fano平面和Aggine Space $（\ Mathbb {Z} _2 _2）^3 $有关。这也允许提供出色的谎言超级甲壳虫的结构。
From an octonion algebra $\mathbb{O}$ over a field $k$ of characteristic not two or three, we show that the fundamental representation ${\rm Im}(\mathbb{O})$ of the derivation algebra ${\rm Der}(\mathbb{O})$ and the spinor representation $\mathbb{O}$ of $\mathfrak{so}({\rm Im}(\mathbb{O}))$ are special orthogonal representations. They have particular geometric properties coming from their similarities with binary cubics and we show that the covariants of these representations and their Mathews identities are related to the Fano plane and the affine space $(\mathbb{Z}_2)^3$. This also permits to give constructions of exceptional Lie superalgebras.
