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 n_(n,2) (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 n_(n,2). We also construct a basis for the generalized Casimir invariants of its solvable extension s_(n+1) consisting entirely of rational functions of the chosen invariants of the nilradical.

19 pages; added references, changes mainly in introduction and conclusions, typos corrected; submitted to J. Phys. A, version to be published