2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127716A generalization of the Kauffman tangle algebra is given for Coxeter type Dn. The tangles involve a pole or order 2. The algebra is shown to be isomorphic to the Birman-Murakami-Wenzl algebra of the same type. This result extends the isomorphism between the two algebras in the classical case, which in our set-up, occurs when the Coxeter type is of type A with index n-1. The proof involves a diagrammatic version of the Brauer algebra of type Dn in which the Temperley-Lieb algebra of type Dn is a subalgebra.33 pagesRepresentation TheoryGroup Theory16K20,17Bxx,20F05,20F36,20M05,57Mxxtext