论文标题
反交换代数及其自动形态的群体
Anti-commutative algebras and their groups of automorphisms
论文作者
论文摘要
我们确定在特征性零的字段$ \ mathbb k $上繁殖的正常形式的特征零，具有类似的亚代代代代数家族，是一个类似的旗帜，作为四维非lie二进制二进制谎言代数，因此可以将其视为二元的二元亲属。这些代数是3维nilpotent Lie代数的$ \ Mathbb K $的扩展，同时二维LIE代数的扩展是由二维Abelian代数扩展。我们将它们的自动形态群描述为三维nilpotent lie lie代数的一组亚组的延伸，$ \ mathbb k $。
We determine normal forms of the multiplication of four-dimensional anti-commutative algebras over a field $\mathbb K$ of characteristic zero having an analogous family of flags of subalgebras as the four-dimensional non-Lie binary Lie algebras, and hence can be considered as the closest relatives of binary Lie algebras. These algebras are extensions of $\mathbb K$ by the 3-dimensional nilpotent Lie algebra and at the same time extensions of a two-dimensional Lie algebra by a two-dimensional abelian algebra. We describe their groups of automorphisms as extensions of a subgroup of the group of automorphisms of the three-dimensional nilpotent Lie algebra by $\mathbb K$.
