On the Intersection of Maximal Subalgebras in a Lie Superalgebra
On the Intersection of Maximal Subalgebras in a Lie Superalgebra
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DOI：
10.1142/s1005386709000479
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发表时间：
2009-09
影响因子：
0.3
通讯作者：
Liangyun Chen;Daoji Meng
中科院分区：
文献类型：
--
作者：
Liangyun Chen;Daoji Meng
Racine，Scheiderer，Elduque，Melikyan等人研究了李代数或李超代数的极大子代数及其交，本文的目的是继续这方面的研究，以获得李超代数更深层次的结构定理.本文发展了李超代数的Frattini理论，将巴恩斯的结果推广到李超代数，得到了可解李超代数和幂零李超代数的一些充要条件.此外，还给出了无环李超代数和初等李超代数的一些充要条件.
The maximal subalgebras and their intersection of a Lie algebra or a Lie superalgebra were studied by Racine, Scheiderer, Elduque, Melikyan, et al. The purpose of the present paper is to continue the investigation in order to obtain deeper structure theorems for Lie superalgebras. We develop the Frattini theory for Lie superalgebras, generalize Barnes's results to Lie superalgebras, and obtain some necessary and sufficient conditions for solvable Lie superalgebras and nilpotent Lie superalgebras. Moreover, some necessary and sufficient conditions for ϕ-free Lie superalgebras and elementary Lie superalgebras are given.