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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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:
Journal 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 algebraelementarye-algebraa-algebraalmost algebraicad-semisimplealgebra and number theoryqa mathematics ??
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Deposited On:
20 Dec 2007 13:41
Last Modified:
18 Dec 2023 01:11