Characterizing Nilpotent n-Lie Algebras by Their Multiplier

Abstract

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