ON TENSOR REPRESENTATIONS OF KNOT ALGEBRAS

The fact that a Yang-Baxter operator defines tensor representations of the Artin braid group has been used to construct knot invariants. The main purpose of this note is to extend the tensor representations of the Artin braid group to representations of the braid group ZB(k) asso ciated to the Coxeter graph B-k. This extension is based on some funda mental identities for the standard R-matrices of quantum Lie theory, h ere called four braid relations. As an application, tensor representat ions of knot algebras of type B (Hecke, Temperley-Lieb, Birman-Wenzl-M urakami) are derived.