Dynkin图与Kantor对的短Peirce分次
Dynkin Diagrams and Short Peirce Gradings of Kantor Pairs
摘要：
在Oleg Smirnov最近的一篇文章中，我们定义了短Peirce（SP）分次Kantor对。对于任何这样的对P，我们定义了一个家庭，参数化的外尔群的类型BC_2，由SP-分次Kantor对称为Weyl图像的P。在这篇文章中，我们分类有限维简单SP-分次Kantor对的代数闭域的特征为0的标记Dynkin图，我们展示了如何计算Weyl图像使用这些图。该理论是特别有吸引力的接近约旦Kantor对（这是变化的Freudenthal三元系），我们构建这样的对的反射（与非平凡的分级）从约旦矩阵对。
英文摘要：
In a recent article with Oleg Smirnov, we defined short Peirce (SP) graded Kantor pairs. For any such pair P, we defined a family, parameterized by the Weyl group of type BC_2, consisting of SP-graded Kantor pairs called Weyl images of P. In this article, we classify finite dimensional simple SP-graded Kantor pairs over an algebraically closed field of characteristic 0 in terms of marked Dynkin diagrams, and we show how to compute Weyl images using these diagrams. The theory is particularly attractive for close-to-Jordan Kantor pairs (which are variations of Freudenthal triple systems), and we construct the reflections of such pairs (with nontrivial gradings) starting from Jordan matrix pairs.
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