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3-Lie algebras with an ideal $N$. (English) Zbl 1178.17004
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.

17A42Other $n$-ary compositions $(n \ge 3)$
17B60Lie (super)algebras associated with other structures
17B30Solvable, nilpotent Lie (super)algebras
Full Text: DOI
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