Fiona Torzewska

Classification of charge conserving loop-braid representations.

The loop braid category is a generalisation of the classical braid category whose morphisms correspond to classes of motions of unknotted, unlinked loops in 3-dimensional space. A loop-braid representation is a monoidal functor from the loop-braid category LB, into Mat. Classification of representations of the loop-braid category is in general hard, as with the braid category. However, progress has been made by restricting the target category. Given a monoidal category C, a rank-N charge-conserving representation is a monoidal functor from C to the category MatchN of rank-N charge-conserving matrices. Here I will discuss the construction of all charge-conserving loop braid representations, and their classification up to suitable notions of isomorphism.