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### Reflective centers of module categories and quantum K-matrices

**Algebra & Discrete Mathematics**

Speaker: | Milen Yakimov, Northeastern University |

Related Webpage: | https://yakimov.sites.northeastern.edu/ |

Location: | 2112 MSB |

Start time: | Tue, Apr 9 2024, 11:00AM |

Braided monoidal categories have applications in various situations, in particular their universal R-matrices give solutions of the quantum Yang-Baxter equation and representations of braid groups of type A. There are powerful methods for constructing them: Drinfeld doubles of Hopf algebras and Drinfeld centers of monoidal categories. On the other hand, universal K-matrices, leading to solutions of the reflection equation and representations of braid groups of type B are much less well understood. We will describe a construction of reflective centers of module categories. It gives rise to braided module categories and a quantum double construction for universal K-matrices. This is a joint work with Robert Laugwitz and Chelsea Walton.