The question of existence of n-ary systems playing the role of enveloping algebras for Filippov (n-Lie) algebras is investigated. We consider the ternary algebras whose reduced binary algebras are associative, the associative algebras, and two other classes of ternary algebras as possible enveloping algebras.

We show that there exist no simple finite-dimensional Filippov superalgebras of type B(0,n) over an algebraically closed field of characteristic 0.

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It is proved that any finite-dimensional n-ary commutative Leibniz algebra over a field of characteristic 0 is solvable.