Characterization of capable nilpotent n-Lie algebras of class two by their Schur multipliers

Abstract

In this paper, we classify the generalized Heisenberg nilpotent n-Lie algebras of rank two with dimension at most $$2n+3$$ . Using them, we classify capable nilpotent n-Lie algebras with two-dimensional derived subalgebra. We also obtain the dimension of the Schur multiplier of nilpotent n-Lie algebras of class two with two-dimensional derived subalgebra.