Leibniz algebras |${\mathcal E}_n$| were introduced as an algebraic structure underlying U-duality. Algebras |${\mathcal E}_3$| derived from Bianchi 3D Lie algebras are classified here. Two types of algebras are obtained: 6D Lie algebras that can be considered an extension of the semi-Abelian 4D Drinfel’d double and unique extensions of non-Abelian Bianchi algebras. For all of the algebras explicit forms of generalized frame fields are given.

中文翻译：

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6D Leibniz代数的分类

莱布尼兹代数| $ {\ mathcal E} _n $ | 被引入作为U-对偶的基础的代数结构。代数| $ {\ mathcal E} _3 $ | 源自Bianchi 3D Lie代数的分类在这里。获得了两种类型的代数：6D Lie代数，可以将其视为半阿贝尔4D Drinfel'd double的扩展，以及非阿贝尔Bianchi代数的唯一扩展。对于所有代数，给出了广义框架域的显式形式。