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

Abstract

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.