E $_{6(6)}$例外Drinfel'd代数
E$_{6(6)}$ Exceptional Drinfel'd Algebras
摘要：
例外Drinfel'd代数（EDA）是一个莱布尼茨代数，用来提供一个代数基础来探索M-理论中U-对偶的广义概念。从本质上讲，它提供了一个M-理论模拟的方式，一个Drinfel'd双重编码广义的T-对偶字符串。本文详细讨论了正则U-对偶群为$E_{6(6)}$时EDA的构造。我们展示了如何EDA可以实现几何作为一个广义的莱布尼茨平行化的特殊广义切丛的六维组流形$G$，赋予一个Nambu李结构。当EDA是共边界型，我们展示了如何自然的推广的经典杨巴克斯特方程出现。该结构说明了一个选择的例子，包括一些嵌入Drinfel'd双打和其他人不是这种类型。
英文摘要：
The exceptional Drinfel'd algebra (EDA) is a Leibniz algebra introduced to provide an algebraic underpinning with which to explore generalised notions of U-duality in M-theory. In essence it provides an M-theoretic analogue of the way a Drinfel'd double encodes generalised T-dualities of strings. In this note we detail the construction of the EDA in the case where the regular U-duality group is $E_{6(6)}$. We show how the EDA can be realised geometrically as a generalised Leibniz parallelisation of the exceptional generalised tangent bundle for a six-dimensional group manifold $G$, endowed with a Nambu-Lie structure. When the EDA is of coboundary type, we show how a natural generalisation of the classical Yang-Baxter equation arises. The construction is illustrated with a selection of examples including some which embed Drinfel'd doubles and others that are not of this type.
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