2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/197971We show that the structure constants of $k$-Lie algebras, $k>3$, with a positive definite metric are the sum of the volume forms of orthogonal $k$-planes. This generalizes the result for $k=3$ in arXiv:0804.2662 and arXiv:0804.3078, and confirms a conjecture in math/0211170.4 pages, minor changes and a reference addedHigh Energy Physics - Theorytext