2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63842The faithfulness of the orthogonal group case of Brauer's representation of the Brauer centralizer algebras restricted to their Temperley-Lieb subalgebras, which was established by Vaughan Jones, is here proved in a new, elementary and self-contained, manner.10 pages, minor correctionsGeometric Topology57M99, 15A03, 16G99, 05C50text