Quasi-filiform Leibniz algebras of maximum length

The n-dimensional p-filiform Leibniz algebras of maximum length have already been studied with 0 ≤ p ≤ 2. For Lie algebras whose nilindex is equal to n-2 there is only one characteristic sequence, (n - 2, 1, 1), while in Leibniz theory we obtain the two possibilities: (n - 2, 1, 1) and (n - 2, 2). The first case (the 2-filiform case) is already known. The present paper deals with the second case, i. e., quasi-filiform non-Lie-Leibniz algebras of maximum length. Therefore this work completes the study of the maximum length of the Leibniz algebras with nilindex n - p with 0 ≤ p ≤ 2. © 2011 Pleiades Publishing, Ltd.