Characterizing Nilpotent n-Lie Algebras by Their Multiplier

Abstract

For every nilpotent n-Lie algebra A of dimension d, t(A) is defined by $$t(A)=\left( {\begin{array}{c}d\\ n\end{array}}\right) -\dim {\mathcal {M}}(A)$$ , where $${\mathcal {M}}(A)$$ denotes the Schur multiplier of A. In this paper, we classify all nilpotent n-Lie alegbras A satisfying $$t(A)=9,10$$ . We also classify all nilpotent n-Lie algebras for $$11\le t(A)\le 16$$ when $$n\ge 3$$ .