3-Lie algebras with an ideal N☆
3-Lie algebras with an ideal N☆
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DOI：
10.1016/j.laa.2009.03.018
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发表时间：
2009-08
影响因子：
1.1
通讯作者：
R. Bai;Caixia Shen;Yao-Z Zhang
中科院分区：
文献类型：
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作者：
R. Bai;Caixia Shen;Yao-Z Zhang
定义了n-李代数中的次幂零理想，得到了m维最简丝状3-李代数为极大次幂零理想的所有可解3-李代数。证明了这类可解3-李代数的维数至多为m+2，且不存在以最简单的丝状3-李代数为零根的可解3-李代数.
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.