A new method for classifying complex filiform Lie algebras (Q1854996)

The authors propose an alternative computational procedure to classify nilpotent Lie algebras, more concretely those of maximal nilindex, also called filiform following \textit{M. Vergne} [Bull. Soc. Math. Fr. 98, 81-116 (1970; Zbl 0244.17011)]. In contrast to other methods used in the literature, here the authors focus on conditions ensuring that certain transformations of a Lie algebra lead to another element lying in the same orbit. This allows them to predict the number of parametrized families appearing for each fixed dimension (the dimensions \(n\leq 14\) are commented upon at the end of the paper).