## 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.

### MSC:

 17A42 Other $$n$$-ary compositions $$(n \ge 3)$$ 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.) 17B30 Solvable, nilpotent (super)algebras
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### References:

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