Basic Commutators in n-Lie Algebras

In this paper, we give the structure of free n-Lie algebras. Next, we introduce basic commutators in n-Lie algebras and generalize the Witt formula to calculate the number of the basic commutators. Also, we prove that the set of all of the basic commutators of weight w and length n+(w-2)(n-1) is a basis for Fw, where Fw is the wth term of the lower central series in the free n-Lie algebra F.