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- 10.1017/S0013091509001035
Final published version

Research output: Contribution to journal › Journal article

Published

<mark>Journal publication date</mark> | 1/06/2011 |
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<mark>Journal</mark> | Proceedings of the Edinburgh Mathematical Society |

Issue number | 2 |

Volume | 54 |

Number of pages | 12 |

Pages (from-to) | 531-542 |

<mark>State</mark> | Published |

<mark>Original language</mark> | English |

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.

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.