论文标题
六维leibniz代数$ {\ Mathcal E} _3的分类
Classification of six-dimensional Leibniz algebras ${\mathcal E}_3
论文作者
论文摘要
Leibniz代数$ {\ MATHCAL E} _n $被引入为u二维的代数结构。代数$ {\ MATHCAL E} _3 $从Bianchi衍生的三维LIE代数在此处进行分类。获得了两种类型的代数：可以认为是非亚伯式bianchi代数的半二维Drinfeld双重和独特扩展的六维式代数。对于所有代数形式，都给出了广义帧场的明确形式。
Leibniz algebras ${\mathcal E}_n$ were introduced as algebraic structure underlying U-duality. Algebras ${\mathcal E}_3$ derived from Bianchi three-dimensional Lie algebras are classified here. Two types of algebras are obtained: Six-dimensional Lie algebras that can be considered extension of semi-Abelian four-dimensional Drinfeld double and unique extensions of non-Abelian Bianchi algebras. For all of the algebras explicit forms of generalized frame fields are given.
