  An infinite filiform Lie algebra L is residually nilpotent and its graded
associated with respect to the lower central series has smallest possible
dimension in each degree but is still infinite. This means that gr(L) is of
dimension two in degree one and of dimension one in all higher degrees. We
prove that if L is solvable, then already [L,L] is abelian. The isomorphism
classes in this case are given in a paper by Bratzlavsky, but the proof there
is incomplete. We make the necessary additional computations and restate
Bratzlavskys result when the ground field is the complex numbers.
