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

Research output: Contribution to journalJournal article

Published

<mark>Journal publication date</mark>1/06/2011
<mark>Journal</mark>Proceedings of the Edinburgh Mathematical Society
Issue2
Volume54
Number of pages12
Pages531-542
<mark>Original language</mark>English

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.

Bibliographic note

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.