On dimension of Lie Algebras and nilpotent Lie algebras

Schur proved that if the center of a group G has finite index, then the derived subgroup G′ is also finite. Moneyhun proved that if L is a Lie algebra such that dim(L/Z(L)) = n, then dim(L^۲) ≤۱/۲n(n-۱) In this paper, we extend the converse of Moneyhun’s theorem. Also, we prove a wellknown result of nilpotent Lie algebras by using a different technique

Keywords:

Nilpotent Lie algebra , Derived subalgebra , Frattini subalgebra