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Two Generator Subalgebras Of Lie Algebras.

Bowman, Kevin and Towers, David A. and Varea, Vicente R. (2007) Two Generator Subalgebras Of Lie Algebras. Linear and Multilinear Algebra, 55 (5). pp. 429-438. ISSN 0308-1087

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    Abstract

    In [14] Thompson showed that a finite group G is solvable if and only if every twogenerated subgroup is solvable (Corollary 2, p. 388). Recently, Grunevald et al. [10] have shown that the analogue holds for finite-dimensional Lie algebras over infinite fields of characteristic greater than 5. It is a natural question to ask to what extent the two-generated subalgebras determine the structure of the algebra. It is to this question that this paper is addressed. Here, we consider the classes of strongly-solvable and of supersolvable Lie algebras, and the property of triangulability.

    Item Type: Article
    Journal or Publication Title: Linear and Multilinear Algebra
    Additional Information: The final, definitive version of this article has been published in the Journal, Linear and Multilinear Algebra, 55 (5), 2007, © Informa Plc
    Uncontrolled Keywords: Lie algebra ; two generator ; solvable ; supersolvable ; triangulable
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 872
    Deposited By: Dr David A. Towers
    Deposited On: 20 Dec 2007 13:54
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Oct 2013 12:44
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/872

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