Non-semisimple tensor categories and topological field theory

Project description

Tensor products play an important role in representation theory and in several of its applications to mathematical physics. From an algebraic point of view, representations of Hopf algebras, such as quantum groups, give interesting examples of tensor categories. Certain classes of tensor categories, called modular categories are of particular interest as they can used to construct 3D topological quantum field theories (TQFTs). In most of the literature, modular categories are fusion, i.e. semisimple. Recently, several of the applications of modular categories have been extended to the non-semisimple case, including constructions of modular functors, mapping class group actions, and 3D TQFTs. Therefore, it is an interesting question to construct more examples of such modular categories that are non-semisimple. Several questions remain to be explored in this direction.