Capable n-Lie algebras and the classification of nilpotent n-Lie algebras with s(A)=3

Darabi et al. (2016) associate to each d-dimensional nilpotent n-Lie algebra A, a number s(A) where s(A)=(d−1n)+n−1−dimM(A) and M(A) denotes the multiplier of A. They prove that s(A) is non-negative and classify all nilpotent n-Lie algebras A for which s(A)=0,1,2. In this paper, we will classify all capable n-Lie algebras with 1-dimensional derived subalgebra and apply it to obtain a classification of those nilpotent n-Lie algebras satisfying s(A)=3.