Furstenberg boundary of a discrete quantum group

Abstract: The notion of topological boundary actions has recently found striking applications in the study of operator algebras associated to discrete groups. We will discuss the analogue concept for discrete quantum groups, show that in this generalization there still always exists a maximal boundary action - the so-called Furstenberg boundary. We discuss applications in problems of C*-simplicity and uniqueness of the Haar state of the dual.

This is joint work with Pawel Kasprzak, Adam Skalski and Roland Vergnioux.

operator algebrasquantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This 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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