On dimension of Lie Algebras and nilpotent Lie algebras

Document Type : Original Article


Department of mathematics, Islamic Azad university, Neyshabour branch, Mashhad, Iran


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^2) ≤1/2n(n-1) 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


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