Towers, David A. (2013) *Supplements to maximal subalgebras of Lie algebras.* Communications in Algebra, 41 (10). pp. 3848-3857. ISSN 0092-7872

## Abstract

For a Lie algebra L and a subalgebra M of L we say that a subalgebra U of L is a supplement to M in L if L = M +U. We investigate those Lie algebras all of whose maximal subalgebras have abelian supplements, those that have nilpotent supplements, those that have nil supplements, and those that have supplements with the property that their derived algebra is inside the maximal subalgebra being supplemented. For the algebras over an algebraically closed field of characteristic zero in the last three of these classes we find complete descriptions; for those in the first class partial results are obtained.

Item Type: | Article |
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Journal or Publication Title: | Communications in Algebra |

Uncontrolled Keywords: | Lie algebras ; maximal subalgebra ; supplement ; solvable ; supersolvable ; Frattini ideal. |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 40727 |

Deposited By: | Dr David A. Towers |

Deposited On: | 21 Apr 2011 09:20 |

Refereed?: | No |

Published?: | Published |

Last Modified: | 18 Oct 2013 09:38 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/40727 |

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