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On semi-modular subalgebras of Lie algebras over fields of arbitrary characteristic.

Towers, David A. (2008) On semi-modular subalgebras of Lie algebras over fields of arbitrary characteristic. Asia-European Journal of Mathematics, 1 (2). pp. 283-294. ISSN 1793-5571

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    Abstract

    This paper is a further contribution to the extensive study by a number of authors of the subalgebra lattice of a Lie algebra. It is shown that, in certain circumstances, including for all solvable algebras, for all restricted Lie algebras over algebraically closed fields of characteristic > 7, and for all Lie algebras having the one-and-a-half generation property, the conditions of modularity and semi-modularity are equivalent, but that the same is not true for all Lie algebras over a field of characteristic three. Semi-modular subalgebras of dimensions one and two are characterised over (perfect, in the case of two-dimensional subalgebras) fields of characteristic different from 2, 3.

    Item Type: Article
    Journal or Publication Title: Asia-European Journal of Mathematics
    Additional Information: Preprint of an article submitted for consideration in Asia-European Journal of Mathematics © 2008 [copyright World Scientific Publishing Company] [http://www.worldscinet.com/aejm/]
    Uncontrolled Keywords: Lie algebra ; subalgebra lattice ; modular ; semi-modular
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 8069
    Deposited By: Dr David A. Towers
    Deposited On: 07 Apr 2008 09:05
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Oct 2013 12:44
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/8069

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