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C-Supplemented Subalgebras of Lie Algebras.

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
    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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