Classification of solvable Lie algebras with a given nilradical by means of solvable extensions of its subalgebras (Q2267413)

\textit{J . L. Rubin} and \textit{P. Winternitz} [J. Phys. A, Math. Gen. 26, No. 5, 1123--1138 (1993; Zbl 0773.17004)] initiated a program in which all solvable Lie algebras, \(S\), with a certain given nilradical, \(N\), are classified. Examples of \(N\) are abelian, Heisenberg or the strictly upper triangular matrices. The present paper is another one in this general program. The algebras considered are denoted by \(n_{n,3}\), have basis \((x_1, ...,x_n)\), \(n \geq 5\) and nonzero multiplication \([x_2,x_n] = x_1, [x_3,x_{n-1}]=x_1\), \([x_k,x_{n-1}]=x_{k-1}\) where \(4 \leq k \leq n-2\), and \( [n_{n-1}, x_n] = x_2\). Over the real or complex numbers the authors show that \(N\) has codimension 1 or 2 in \(S\). In the former case, there are 5 such \(S\) for each \(n \geq 7\) and these algebras are listed. In the latter case, there is only one \(S\) for each \(n \geq 7\) and it is listed.