Braid Group Representations from Twisted Tensor Products of Algebras

Abstract

We unify and generalize several approaches to constructing braid group representations from finite groups, using iterated twisted tensor products. We provide some general characterizations and classification of these representations, focusing on the size of their images, which are typically finite groups. The well-studied Gaussian representations associated with metaplectic modular categories can be understood in this framework, and we give some new examples to illustrate their ubiquity. Our results suggest a relationship between the braiding on the G-gaugings of a pointed modular category ${\mathcal {C}}(A,Q)$ and that of ${\mathcal {C}}(A,Q)$ itself.

Funding

Directorate for Mathematical and Physical Sciences(1664359); Simons Foundation(614735)