2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75203We provide an explicit algorithm to calculate invariant tensors for the adjoint representation of the simple Lie algebra $sl(n)$, as well as arbitrary representation in terms of roots. We also obtain explicit formulae for the adjoint representations of the orthogonal and symplectic Lie algebras $so(n)$ and $sp(n)$.18 pages, 8 figures. To appear in a special issue of Journal of Mathematical SciencesGeometric Topology57M25text