Then a nilpotent Lie algebra has a natural filtration given by the central descending sequence: G = [C.
An n-dimensional nilpotent Lie algebra is called filiform if its nilindex p = n [right arrow] 1.
Thus an n-dimensional nilpotent Lie algebra is filiform if its characteristic sequence is of the form c (G) = (n - 1, 1).
Section 4 is dedicated to nilpotent Lie algebras and specially to filiform Lie algebras.
We have the following characterization of nilpotent Lie algebras (Engel's theorem).
n] of filiform Lie algebras which play an important role in the study of the algebraic varieties of filiform and more generally nilpotent Lie algebras.
The contributors investigate alternating triple systems with simple Lie algebras of derivations, simple decompositions of simple Lie superalgebras, generalized capable abelian groups, Freudenthal's magic square, and Vinberg algebras associated to some nilpotent Lie algebras