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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Solvable complemented Lie algebras


Author: David A. Towers
Journal: Proc. Amer. Math. Soc. 140 (2012), 3823-3830
MSC (2010): Primary 17B05, 17B30; Secondary 17B10, 17B50
Published electronically: March 20, 2012
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Abstract: In this paper a characterisation is given of solvable complemented Lie algebras. They decompose as a vector space direct sum of abelian subalgebras, and their ideals relate nicely to this decomposition. The class of such algebras is shown to be a formation whose residual is the ideal closure of the prefrattini subalgebras.


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Additional Information

David A. Towers
Affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England
Email: d.towers@lancaster.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11244-4
PII: S 0002-9939(2012)11244-4
Keywords: Lie algebras, complemented, solvable, Frattini ideal, prefrattini subalgebra, residual, Lie $A$-algebra.
Received by editor(s): April 20, 2011
Received by editor(s) in revised form: April 26, 2011, and May 8, 2011
Published electronically: March 20, 2012
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.