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We give a bound on the dimension of the Schur multiplier of a finite-dimensional nilpotent  n -Lie algebra, which sharpens the earlier bounds on the dimension of Schur multiplier of such  n -Lie algebras. Then we give the structure of all nilpotent  n -Lie algebras that attain this bound. Also, we obtain a new bound on the dimension of the Schur multiplier of a  d -dimensional  c -step nilpotent  n -Lie algebra with the derived subalgebra of dimension  d  –  n , which sharpens the earlier known bounds.

New bounds on the dimension of the Schur multiplier of n -Lie algebras