Towers, David (2014) *On the lengths of certain chains of subalgebras in Lie algebras.* Communications in Algebra, 42 (11). pp. 4778-4789. ISSN 0092-7872

## Abstract

In this paper we study the lengths of certain chains of subalgebras of a Lie algebra L: namely, a chief series, a maximal chain of minimal length, a chain of maximal length in which each subalgebra is modular in L, and a chain of maximal length in which each subalgebra is a quasi-ideal of L. In particular we show that, over a field F of characteristic zero, a Lie algebra L with radical R has a maximal chain of subalgebras and a chain of subalgebras all of which are modular in L of the same length if and only if L = R, or ??? and L/R is a direct sum of isomorphic three-dimensional simple Lie algebras.

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

Uncontrolled Keywords: | Chief series ; Lie algebras ; Maximal chain ; Modular subalgebra ; Quasi\-ideal |

Subjects: | |

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

ID Code: | 69525 |

Deposited By: | ep_importer_pure |

Deposited On: | 28 May 2014 13:10 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 11 Apr 2018 00:20 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/69525 |

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