New properties of filiform Lie algebras and its computational processing

摘要

In this paper we study a characterization for a complex filiform Lie algebra to be characteristically nilpotent and we also give two new ways of defining complex filiform Lie algebras, by using proper subsets of the set of commutators of the basis elements. Besides, we present three polynomial time algorithms suitable to be used in the study of these results. The first of them allow us to know if a complex filiform Lie algebra is characteristically nilpotent. The other two ones are useful to give two new ways of defining complex filiform Lie algebras by using less non-null brackets than usual.