Arjeh M. Cohen: Algebras related to Links and Tangles

In much the same way the Hecke algebra can be used to construct the Jones polynomial of a knot, the BMW algebra (named after Birman, Murakami, and Wenzl) can be used to construct the Kauffman polynomial of an unoriented link. The braid group is a subgroup of the group of units in this algebra. We shall introduce these notions of knot theory.

The braid groups are well known to be the Artin groups of type A_n. We discuss similar algebras, of type D_n and E_n. We establish the structure of these algebras, and, for type D_n, represent them as algebras of tangles.

The talk is based on joint work with Dié Gijsbers and David Wales.