Solvable Lie algebras with an N-graded nilradical of maximal nilpotency degree and their invariants

The class of solvable Lie algebras with an N-graded nilradical of maximal nilpotency index is classified. It is shown that such solvable extensions are unique up to isomorphism. The generalized Casimir invariants for the N-graded nilradicals and their associated solvable extensions are computed by the method of moving frames.