2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154971In this paper, we compute the Gram determinants associated to each cell module of the Birman-Wenzl algebras. As a by-product, we give the necessary and sufficient condition for semisimple Birman-Wenzl algebras over an arbitrary field.23 pages, we rewrite the paper. In particular, we delete some elementary computation. One can use the GAP program [19] to check the required formulae for small $n$ easilyQuantum AlgebraRepresentation Theory16G99, 20C08text