3 -Lie algebras with an ideal N

We define the hypo-nilpotent ideal in n -Lie algebras and obtain all solvable 3 -Lie algebras with an m -dimensional simplest filiform 3 -Lie algebra as a maximal hypo-nilpotent ideal. We prove that the dimension of such solvable 3 -Lie algebras is at most m + 2 , and there is no solvable 3 -Lie alg...

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Bibliographic Details
Published in:Linear algebra and its applications 2009-08, Vol.431 (5), p.673-700
Main Authors: Bai, Rui-pu, Shen, Cai-hong, Zhang, Yao-zhong
Format: Article
Language:English
Subjects:
[formula omitted]-Lie algebra
Algebra
Exact sciences and technology
Hypo-nilpotent ideal
Linear and multilinear algebra, matrix theory
Mathematics
Nilradical
Sciences and techniques of general use
The simplest filiform n-Lie algebra
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Summary:We define the hypo-nilpotent ideal in n -Lie algebras and obtain all solvable 3 -Lie algebras with an m -dimensional simplest filiform 3 -Lie algebra as a maximal hypo-nilpotent ideal. We prove that the dimension of such solvable 3 -Lie algebras is at most m + 2 , and there is no solvable 3 -Lie algebra with the simplest filiform 3 -Lie algebra as the nilradical.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2009.03.018