Engel subalgebras of n-Lie algebras

Details Engel subalgebras of n-Lie algebras Engel subalgebras of n-Lie algebras

2006-10-10

arxiv.org/abs/math/0610347v1

Acta Math. Sinica 24 (2008) 159--166

Mathematics

Rings and Algebras

9 pages

Scientific paper

Engel subalgebras of finite-dimensional n-Lie algebras are shown to have similar properties to those of Lie algebras. Using these, it is shown that an n-Lie algebra, all of whose maximal subalgebras are ideals, is nilpotent. A primitive 2-soluble n-Lie algebra is shown to split over its minimal ideal and that all the complements to its minimal ideal are conjugate. A subalgebra is shown to be a Cartan subalgebra if and only if it is minimal Engel, provided that the field has sufficiently many elements. Cartan subalgebras are shown to have a property analogous to intravariance.

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