  It will be shown that every N-graded Lie algebra generated in degree 1 of
type FP with entropy less or equal to 1 must be finite-dimensional (cf. Thm.
A). As a consequence every Koszul Lie algebra with entropy less or equal to 1
must be abelian (cf. Cor. C). These results are obtained from a generalized
Witt formula (cf. Thm. D) for N-graded Lie algebras of type FP and the analysis
of necklace polynomials at roots of unity.
