The 2-nilpotent multiplier of n-Lie algebras and its applications

In this paper, we first recall the concept of c-nilpotent multiplier and c-capability of n-Lie algebras and also, recall the formula for calculating the number of basic commutators in n-Lie algebras. Then we give the structure of 2-nilpotent multiplier of the direct sum of two n-Lie algebras. Next, we calculate the dimension of 2-nilpotent multiplier of every abelian n-Lie algebras and Heisenberg n-Lie algebras H(n,m). Then we give a dimension of 2-nilpotent multiplier of any nilpotent n-Lie algebras of class 2 by using the number of basic commutators.