论文标题
koszul lie代数的黑鲁什定理
Kurosh theorem for certain Koszul Lie algebras
论文作者
论文摘要
小组的黑鲁斯定理提供了群体的任何子群体的结构，其证明依赖于作用于树木的小组的低音 - 列理论。在谎言代数的情况下，这种一般理论不存在，而黑鲁斯定理通常是错误的，因为Shirshov首先注意到了。但是，我们证明，对于满足共同体中某些局部特性的一类分级的谎言代数，这种结构定理对于1级中产生的亚代词是正确的。该类别由Lie代数组成，这些代数由lie代数组成，这些代数具有所有的亚代代代代数，该级代数为koszul的$ 1 $ $ 1 $。
The Kurosh theorem for groups provides the structure of any subgroup of a free product of groups and its proof relies on Bass-Serre theory of groups acting on trees. In the case of Lie algebras, such a general theory does not exists and the Kurosh theorem is false in general, as it was first noticed by Shirshov. However, we prove that, for a class of positively graded Lie algebras satisfying certain local properties in cohomology, such a structure theorem holds true for subalgebras generated in degree 1. Such class consists of Lie algebras, which have all the subalgebras generated in degree $1$ that are Koszul.
