Nilpotent Lie algebras in which all proper subalgebras have class at most n, II

Abstract

Let be a field and let L be a finitely generated nilpotent Lie -algebra of class (exactly) c. Let n be the largest integer such that L has a proper subalgebra of class n, and let be the smallest integer such that L can be generated by d elements. In this work, we suppose that . We show that if , then either and L is the unique non-abelian nilpotent Lie -algebra of dimension 3, or the characteristic of is 3, and L is a certain Lie -algebra of dimension 7 in which every maximal subalgera has class 2. We compare this with previous results that deal with the case .