All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n − 1

Abstract

We construct all solvable Lie algebras with a specific n-dimensional nilradical (of degree of nilpotency n − 1 and with an (n − 2)-dimensional maximal Abelian ideal). We find that for given n such a solvable algebra is unique up to isomorphisms. Using the method of moving frames we construct a basis for the Casimir invariants of the nilradical . We also construct a basis for the generalized Casimir invariants of its solvable extension consisting entirely of rational functions of the chosen invariants of the nilradical.