C*-SIMPLICITY AND BOUNDARY ACTIONS OF DISCRETE QUANTUM GROUPS

Speaker(s)

BENJAMIN ANDERSON-SACKANEY

Affiliation

University of Saskatchewan, Saskatoon, Canada

Language of the talk

English

Date

Dec. 11, 2024, 5:15 p.m.

Link

https://uw-edu-pl.zoom.us/j/95105055663?pwd=TTIvVkxmMndhaHpqMFUrdm8xbzlHdz09

Title in Polish

C*-SIMPLICITY AND BOUNDARY ACTIONS OF DISCRETE QUANTUM GROUPS

Seminar

North Atlantic Noncommutative Geometry Seminar

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A group is C*-simple if its reduced C*-algebra is simple. Two of the most historically important notions used for proving a group is C*-simple are Powers’ averaging property and topologically free boundary actions. These techniques led to remarkable dynamical characterizations of C*-simplicity. Besides the establishment of many quantum examples by extending Powers' ideas, little progress has been made on C*-simplicity for quantum groups. In this talk, we will introduce the notion of a strong C*-faithful action of a discrete quantum group which we note that, in the case of a group acting on a topological boundary, is equivalent to topological freeness. We are able to use this notion to recover C*-simplicity of free unitary discrete quantum groups. We will also discuss boundary maps and their involvement with Powers’s averaging property, C*-simplicity, and topological freeness. This talk is based on joint work with Roland Vergnioux.

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