本原李超代数和李超代数的主因子

Primitive Lie Superalgebras and Chief Factors of Lie Superalgebras

本文首先引入了本原李超代数,研究了三种类型本原李超代数及其相关的结构性质.接着引入了李超代数主因子,利用第三种类型的本原李超代数性质给出了李超代数的主因子之间存在的L-连接关系.最后,介绍了李超代数的CAP-子代数,证明了若李超代数L的所有极大阶化子代数都是CAP-子代数,那么L是可解的.

In this paper,we first introduce the concept of primitive Lie superalgebras and investigation three types of primitive Lie superalgebra and some related structural properties.Then,the concept of chief factors of Lie superalgebra is introduced.According to the properties of the third type of primitive Lie superalgebra,the L connection relation between the chief factors of Lie superalgebra is given.Finally,we introduce the CAP-subalgebras of Lie superalgebra L,and prove that L is solvable if all maximal subalgebras of Lie superalgebra are CAP-subalgebras.