Yetter-Drinfeld algebras, module categories and injectivity

Abstract: Many examples of quantum group actions carry a Yetter-Drinfeld structure. Among them, you find C*-algebras coming from the boundary theory of Drinfeld doubles, which is closely related to the theory of ucp maps and injective envelopes of Hamana. Exploring Tannaka-Krein duality for quantum group actions, it is possible to extend many concepts and results of boundary theory to the categorical setting, but the lack of a categorification of non-braided-commutative Yetter-Drinfeld algebras impose an obstruction to a full analogy.

In this talk, I will sketch how to perform such a categorification and relate it to the study of injectivity for module categories. Based on joint works with E. Habbestad, S. Neshveyev and M. Yamashita.

category theoryoperator algebrasquantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This online seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

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