On classification of 7-dimensional odd-nilpotent Leibniz algebras

Abstract

In this paper we extend the method of canonical form for congruence of bilinear forms to give the classification of some subclasses of 7-dimensional nilpotent Leibniz algebras. Odd-nilpotent Leibniz algebras are defined as that its even dimensional ideals in lower central series are all zero and the classification of 7-dimensional complex odd-nilpotent Leibniz algebras with one dimensional Leib ideal is obtained by applying the aforementioned method.