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The index complex of a maximal subalgebra of a Lie algebra

Part of: Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  08 April 2011

David A. Towers
David A. Towers
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK (d.towers@lancaster.ac.uk)
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Abstract

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Let M be a maximal subalgebra of the Lie algebra L. A subalgebra C of L is said to be a completion for M if C is not contained in M but every proper subalgebra of C that is an ideal of L is contained in M. The set I(M) of all completions of M is called the index complex of M in L. We use this concept to investigate the influence of the maximal subalgebras on the structure of a Lie algebra, in particular, finding new characterizations of solvable and supersolvable Lie algebras.

Keywords

Lie algebrasmaximal subalgebraindex complexideal indexsolvablesupersolvable algebra

MSC classification

Secondary: 17B05: Structure theory 17B20: Simple, semisimple, reductive (super)algebras 17B30: Solvable, nilpotent (super)algebras 17B50: Modular Lie (super)algebras
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 2 , June 2011 , pp. 531 - 542
Copyright
Copyright © Edinburgh Mathematical Society 2011

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