SCAP-subalgebras of Lie algebras

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• 作者：Sara Chehrazi ; Ali Reza Salemkar
• 关键词：Lie algebra ; SCAP ; subalgebra ; chief series ; solvable ; supersolvable
• 刊名：Czechoslovak Mathematical Journal
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：66
• 期：4
• 页码：1177-1184
• 全文大小：121 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Convex and Discrete Geometry
  Ordinary Differential Equations
  Mathematical Modeling and IndustrialMathematics
  
• 出版者：Springer Netherlands
• ISSN：1572-9141
• 卷排序：66

文摘

A subalgebra H of a finite dimensional Lie algebra L is said to be a SCAP-subalgebra if there is a chief series 0 = L₀ ⊂ L₁ ⊂... ⊂ L_t = L of L such that for every i = 1, 2,..., t, we have H + L_i = H + L_i-1 or H ∩ L_i = H ∩ L_i-1. This is analogous to the concept of SCAP-subgroup, which has been studied by a number of authors. In this article, we investigate the connection between the structure of a Lie algebra and its SCAP-subalgebras and give some sufficient conditions for a Lie algebra to be solvable or supersolvable.