Lancaster EPrints

Supplements to maximal subalgebras of Lie algebras

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

[img]
Preview
PDF (supplements_of_maximals.pdf) - Draft Version
Download (148Kb) | Preview

    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
    Journal or Publication Title: Communications in Algebra
    Additional Information: The final, definitive version of this article has been published in the Journal, Communications in Algebra, 41 (10), 2013, © Informa Plc
    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: 13 Jun 2014 09:37
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/40727

    Actions (login required)

    View Item