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Zbl 1178.17004
Bai, Ruipu; Shen, Caihong; Zhang, Yaozhong
3-Lie algebras with an ideal $N$. (English)
[J] Linear Algebra Appl. 431, No. 5-7, 673-700 (2009). ISSN 0024-3795

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.

MSC 2000:: *17A42 Other n-ary compositions
17B60 Lie rings associated with other structures
17B30 Solvable, nilpotent Lie algebras

Keywords: 3-Lie algebra; hypo-nilpotent ideal; nilradical; simplest filiform $n$-Lie algebra

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	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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