Braid group representations from twisted tensor products of algebras

TL;DR

This paper introduces a unified framework for constructing braid group representations using iterated twisted tensor products of algebras, revealing potential links between braidings in certain modular categories.

Contribution

It generalizes existing methods for braid group representations by employing twisted tensor products, connecting different categorical structures.

Findings

Unified approach to braid group representations

Potential relationship between braidings in gaugings and original categories

Generalization of previous algebraic constructions

Abstract

We unify and generalize several approaches to constructing braid group representations from finite groups, using iterated twisted tensor products. Our results hint at a relationship between the braidings on the $G$-gaugings of a pointed modular category $\mathcal{C}(A,Q)$ and that of $\mathcal{C}(A,Q)$ itself.