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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.
MSC:
17A42Other n-ary compositions (n3)
17B60Lie (super)algebras associated with other structures
17B30Solvable, nilpotent Lie (super)algebras
References:
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