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Journal of Lie Theory 24 (2014), No. 4, 969--978
Copyright Heldermann Verlag 2014

On Certain Decompositions of Solvable Lie Algebras

David A. Towers
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England

The author has previously shown that solvable Lie A-algebras and complemented solvable Lie algebras decompose as a vector space direct sum of abelian subalgebras, and their ideals relate nicely to this decomposition. However, neither of these classes is contained in the other. The object of this paper is to find a larger class of algebras, containing each of these classes, in which these same results hold.

Keywords: Lie algebras, solvable, completely completely solvable, A-algebras, complemented, splitting, monolithic, Frattini ideal.

MSC: 17B05, 17B20, 17B30, 17B50

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