2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54304By explicit calculation, I determine the structure of the ground ring of the critical $W_3$ gravity and show that there is an $su(3)$ invariant quadratic relation among the six basic elements. By using this result, I also construct some discrete physical states of the critical $W_3$ gravity.10 pages, LaTeX (elsart)High Energy Physics - Theorytext