A new method for classifying complex filiform Lie algebras

Abstract

In this paper, we describe a new method to classify complex filiform Lie algebras based on the concept of isomorphism between Lie algebras. This method, which has the advantage of being applied to any dimension, gives the families of algebras in each dimension in an explicit way. In order to apply, only the corresponding structure the- orem of complex filiform Lie algebras in each dimension is needed. As a consequence of our study, we also predict that the increase (in terms of quotiens) in the number of algebras families when passing from even dimension to odd dimension tends to 1 whereas it grows in a no finite way if passing from odd dimension to immediate even dimension.