Towers, David A. (2008) *C-Supplemented Subalgebras of Lie Algebras.* Journal of Lie Theory, 18 (3). pp. 717-724. ISSN 0949-5932

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## Abstract

A subalgebra $B$ of a Lie algebra $L$ is c-{\it supplemented} in $L$ if there is a subalgebra $C$ of $L$ with $L = B + C$ and $B \cap C \leq B_L$, where $B_L$ is the core of $B$ in $L$. This is analogous to the corresponding concept of a c-supplemented subgroup in a finite group. We say that $L$ is c-{\it supplemented} if every subalgebra of $L$ is c-supplemented in $L$. We give here a complete characterisation of c-supplemented Lie algebras over a general field.

Item Type: | Article |
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Journal or Publication Title: | Journal of Lie Theory |

Uncontrolled Keywords: | Lie algebras ; c-supplemented subalgebras ; completely factorisable algebras ; Frattini ideal ; subalgebras of codimension one. |

Subjects: | Q Science > QA Mathematics |

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

ID Code: | 860 |

Deposited By: | Dr David A. Towers |

Deposited On: | 19 Dec 2007 16:06 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 09 Oct 2013 12:43 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/860 |

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