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

The class of solvable Lie algebras with an -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 -graded nilradicals and their associated solvable extensions are computed by the method of moving frames.

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