This master project is about the relation between the representation of type B braid groups and associated tensor categorical structures. The relation between type A braid groups, braided categories, and quantum field theories was an important guiding principle that led to many developments in mathematics and theoretical physics in the last 30 years. The type B braid group, which is given by the usual type A braid group and an extra generator, corresponds to the quantum field theories with boundary, and the braided module categories. Our goal is to find new examples of braided module categories (or equivalent structures such as algebra objects with ribbon braid), and to understand the induced representations of type B braid groups. We will also look at the problem of universality, that is, whether the images of these representations are dense in the projective model of the intertwiner spaces. This is expected to have application to quantum computation.
Prerequisite knowledge: