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Engel Subalgebras of n-Lie Algebras
作者姓名:Donald  W.  BARNES
作者单位:Little Wonga Rd, Cremorne NSW 2090 Australia
基金项目:This work was done while the author was an Honorary Associate of the School of Mathematics and Statistics, University of Sydney
摘    要: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 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.

关 键 词:子代数  幂零  数学分析  求解方法
收稿时间:2006-03-09
修稿时间:2006-12-29

Engel subalgebras of <Emphasis Type="Italic">n</Emphasis>-Lie algebras
Donald W. BARNES.Engel Subalgebras of n-Lie Algebras[J].Acta Mathematica Sinica,2008,24(1):159-166.
Authors:Donald W Barnes
Institution:(1) 1 Little Wonga Rd, Cremorne, NSW, 2090, Australia
Abstract: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 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.
Keywords:n-Lie algebras  soluble  nilpotent  Engel subalgebras
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