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Elementary Lie Algebras and Lie A-Algebras.

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

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    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: 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: Q Science > QA Mathematics
    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: 09 Oct 2013 12:44
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/871

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