Towers, David A. and Varea, Vicente R. (2007) *Elementary Lie Algebras and Lie A-Algebras.* Journal of Algebra, 312 (2). pp. 891-901.

## Abstract

A finite-dimensional Lie algebra L over a field F is called elementary if each of its subalgebras has trivial Frattini ideal; it is an A-algebra if every nilpotent subalgebra is abelian. The present paper is primarily concerned with the classification of elementary Lie algebras. In particular, we provide a complete list in the case when F is algebraically closed and of characteristic different from 2,3, reduce the classification over fields of characteristic 0 to the description of elementary semisimple Lie algebras, and identify the latter in the case when F is the real field. Additionally it is shown that over fields of characteristic 0 every elementary Lie algebra is almost algebraic; in fact, if L has no non-zero semisimple ideals, then it is elementary if and only if it is an almost algebraic A-algebra.

Item Type: | Journal Article |

Journal or Publication Title: | Journal of Algebra |

Additional Information: | The final, definitive version of this article has been published in the Journal, Journal of Algebra 312 (2), 2007, © ELSEVIER. |

Uncontrolled Keywords: | Lie algebra ; elementary ; E-algebra ; A-algebra ; almost algebraic ; ad-semisimple |

Subjects: | ?? qa ?? |

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

ID Code: | 871 |

Deposited By: | Dr David A. Towers |

Deposited On: | 20 Dec 2007 13:41 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 28 May 2018 00:14 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/871 |
---|

### Actions (login required)