映射E6组的几何结构
Mapping the geometry of the E6 group
摘要：
本文通过对相应的李代数e6进行指数化，给出了例外李群E6的紧形式的一个构造，并将其表示为f4的和、3维例外Jordan代数J3的八元导子以及J3的迹为零的元素的右乘.我们的参数化是SU（2）的欧拉角的推广，并且它基于E6通过F4子群作为纤维的纤维化。它使用了我们在前一篇文章中为F4执行的类似构造。这些结果的一个有趣的第一个应用在于这样一个事实，即我们能够确定一个明确的表达Haar不变测度的E6组流形。
英文摘要：
In this paper we present a construction for the compact form of the exceptional Lie group E6 by exponentiating the corresponding Lie algebra e6, which we realize as the the sum of f4, the derivations of the exceptional Jordan algebra J3 of dimension 3 with octonionic entries, and the right multiplication by the elements of J3 with vanishing trace. Our parametrization is a generalization of the Euler angles for SU(2) and it is based on the fibration of E6 via a F4 subgroup as the fiber. It makes use of a similar construction we have performed in a previous article for F4. An interesting first application of these results lies in the fact that we are able to determine an explicit expression for the Haar invariant measure on the E6 group manifold.
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