Title: The three layers of a braided fusion category: Core, Mantle, and Crust
Speaker: Dmitri Nikshych (University of New Hampshire)
Abstract: The main objects of this talk are semisimple categories with tensor products satisfying a commutativity constraint (braiding). Examples of such categories come from classical sources (representations of groups and Hopf algebras) and quantum ones such as affine Lie algebras and exotic subfactors. When one separates the group-theoretical and quantum parts of a braided fusion category C, several interesting invariants appear. One such invariant is the core defined as the localization of C by a maximal Tannakian subcategory. Another is the mantle of C, which is the localization of C by its Tannakian radical (the “crust”). I will explain how to approach the classification of braided fusion categories using these invariants and a certain gauging procedure. This is based on a joint work with Jason Green.
