Weak Quasi-Hopf Algebras Associated to Verlinde Fusion Categories

Explore a 33-minute conference talk on weak quasi-Hopf algebras associated with Verlinde fusion categories, presented by Claudia Pinzari from Sapienza Università di Roma. Delve into the world of unitary modular fusion categories, focusing on those with Verlinde fusion rules arising from quantum groups at roots of unity. Discover the concept of weak quasi-Hopf algebras, introduced by Mack and Schomerus as an extension of Drinfeld's quasi-Hopf algebras. Learn about the association of semisimple weak quasi-Hopf algebras to fusion categories, following Wenzl's ideas for all Lie types. Gain insights into a potential direct proof of the Kazhdan-Lusztig-Finkelberg theorem. This talk, part of the "Actions of Tensor Categories on C*-algebras 2021" series at the Institute for Pure and Applied Mathematics (IPAM), UCLA, offers a comprehensive overview of unitarity and explores the collaborative work of Pinzari with S. Carpi, S. Ciamprone, and M.V. Giannone.