Maximal subalgebras and chief factors of Lie algebras

Towers, David (2016) Maximal subalgebras and chief factors of Lie algebras. Journal of Pure and Applied Algebra, 220 (1). pp. 482-493. ISSN 0022-4049

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Abstract

This paper is a continued investigation of the structure of Lie algebras in relation to their chief factors, using concepts that are analogous to corresponding ones in group theory. The first section investigates the structure of Lie algebras with a core-free maximal subalgebra. The results obtained are then used in section two to consider the relationship of two chief factors of L being L-connected, a weaker equivalence relation on the set of chief factors than that of being isomorphic as L-modules. A strengthened form of the Jordan-H�older Theorem in which Frattini chief factors correspond is also established for every Lie algebra. The final section introduces the concept of a crown, a notion introduced in group theory by Gasch�utz, and shows that it gives much information about the chief factors

Item Type:
Journal Article
Journal or Publication Title:
Journal of Pure and Applied Algebra
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2602
Subjects:
ID Code:
74108
Deposited By:
Deposited On:
18 Jun 2015 06:02
Refereed?:
Yes
Published?:
Published
Last Modified:
12 Jul 2020 05:07