2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161734The cyclotomic Birman-Wenzl-Murakami algebras are quotients of the affine BMW algebras in which the affine generator satisfies a polynomial relation. We study admissibility conditions on the ground ring for these algebras, and show that the algebras defined over an admissible integral ground ring $S$ are free $S$--modules and isomorphic to cyclotomic Kauffman tangle algebras. We also determine the representation theory in the generic semisimple case, obtain a recursive formula for the weights of the Markov trace, and give a sufficient condition for semisimplicity.Stylistic corrections; changed numbering of sections; changed titleQuantum AlgebraRepresentation Theory20C08, 81R50, 16G99text