SOLVABLE INDECOMPOSABLE EXTENSIONS OF TWO NILPOTENT LIE ALGEBRAS

A pair of sequences of nilpotent Lie algebras denoted by N-n,N- 7 and N-n,N- 16 are introduced. Here, n denotes the dimension of the algebras that are defined for n6; the first terms in the sequences are denoted by 6.7 and 6.16, respectively, in the standard list of six-dimensional Lie algebras. For each of them, all possible solvable extensions are constructed so that N-n,N- 7 and N-n,N- 16 serve as the nilradical of the corresponding solvable algebras. The construction continues Winternitz' and colleagues' program of investigating solvable Lie algebras using special properties rather than trying to extend one dimension at a time.