Relations among invariants of complex filiform Lie algebras

摘要

Apart from the own dimension n of a complex filiform Lie algebra, the first invariant known for these algebras was the lower central sequence of the algebra, obtained by Ancochea and Goze in 1989. Later, Echarte, Gómez and Núñez, in 1996, and ourselves, in the same year, obtained the invariants i and j, respectively. In this paper, we prove new properties of the invariant j and we use them to set some relations among these invariants and the dimension n. These results allow us to classify complex filiform Lie algebras according to some values of those invariants.