Infinite-Dimensional Algebra Seminar: Milen Yakimov (Northeastern)

Building 2, Room 135

Speaker: Milen Yakimov (Northeastern University)Where: In-Person at MIT Room 2-135 and onZoom https://mit.zoom.us/j/94469771032?pwd=d3JaSVhVV0xDOGpkUDdveXdOYmNXQT09Title: Reflective centres of module categories and quantum K-matricesAbstract: 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 centres 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 (a la Drinfeld) for universal K-matrices. From this perspective, quantum R-matrices come from categorical versions of centers of algebras and quantum K-matrices come from categorical versions of centers of bimondules. This is a joint work with Robert Laugwitz and Chelsea Walton.