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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Official URL: http://dx.doi.org/10.1017/S0013091509001035

## 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 |
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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: | 22 Jan 2017 01:33 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/27158 |

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