Naturally graded quasi-filiform Leibniz algebras

摘要

The classification of naturally graded quasi-filiform Lie algebras is known; they have the characteristic sequence (n - 2, 1. 1) where n is the dimension of the algebra. In the present paper we deal with naturally graded quasi-filiform non-Lie-Leibniz algebras which are described by the characteristic sequence C(￡) = (n -2. 1. 1) or C(￡) = (n - 2, 2). The first case has been studied in [Camacho, L.M., Gomez, J.R., Gonzalez, A.J., Omirov, B.A., 2006. Naturally graded 2-filiform Leibniz Algebra and its applications, preprint. MA1-04-XI06] and now, we complete the classification of naturally graded quasi-filiform Leibniz algebras. For this purpose we use the software Mathematica (the program used is explained in the last section).