A characterization of finite dimensional nilpotent Filippov algebras

Let A be a nilpotent Filippov (n-Lie) algebra of dimension d and put s(A)=(d−1n)+n−1−dimM(A) and t(A)=(dn)−dimM(A), where M(A) denotes the multiplier of A. The aim of this paper is to classify all nilpotent n-Lie algebras A for which s(A)=0, 1 or 2, and apply it in order to determine all nilpotent n-Lie algebras A satisfying 0≤t(A)≤8.