Nilpotent Lie algebras of maximal rank and of Kac-Moody type: \(E_{6}^{(1)}\) (Q1604365)

\textit{L. J. Santharoubane} has shown [Can. J. Math. 34, 1215-1239 (1982; Zbl 0495.17011)] that for each nilpotent Lie algebra there is an associated Kac-Moody Lie algebra and used this correspondence to classify those of the former associated with certain of the latter. This method has been used by various authors to study nilpotent Lie algebras of maximal rank associated with classical simple type and type \(E_6\), \(E_7\), \(E_8\), \(A_2^{(1)}\), \(B_2^{(2)}\), \(G_2^{(2)}\) and \(F_4^{(1)}\). This paper deals with \(E_6^{(1)}\).