The index complex of a maximal subalgebra of a Lie algebra.

Towers, David A. (2011) The index complex of a maximal subalgebra of a Lie algebra. Proceedings of the Edinburgh Mathematical Society, 54 (2). pp. 531-542. ISSN 0013-0915

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Abstract

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 characterisations of solvable and supersolvable Lie algebras.

Item Type:
Journal Article
Journal or Publication Title:
Proceedings of the Edinburgh Mathematical Society
Additional Information:
http://journals.cambridge.org/action/displayJournal?jid=PEM The final, definitive version of this article has been published in the Journal, Proceedings of The Edinburgh Mathematical Society, 54 (2), pp 531-542 2011, © 2011 Cambridge University Press.
Uncontrolled Keywords:
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Subjects:
ID Code:
27158
Deposited By:
Deposited On:
05 Oct 2009 14:06
Refereed?:
Yes
Published?:
Published
Last Modified:
11 Aug 2020 00:11