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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: 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: Lie algebras ; maximal subalgebra ; index complex ; ideal index ; solvable ; supersolvable ; Frattini ideal.
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 27158
    Deposited By: Dr David A. Towers
    Deposited On: 05 Oct 2009 15:06
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Oct 2013 12:44
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/27158

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