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: /dk/atira/pure/researchoutput/libraryofcongress/qa
Subjects:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 27158
Deposited By: Dr David A. Towers
Deposited On: 05 Oct 2009 14:06
Refereed?: Yes
Published?: Published
Last Modified: 18 Sep 2019 00:29
URI: https://eprints.lancs.ac.uk/id/eprint/27158

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