##### Department of Mathematics,

University of California San Diego

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### Math 243 - Functional Analysis Seminar

## Mehrdad Kalantar

#### University of Houston

## Noncommutative boundary maps and C*-algebras of quasi-regular representations

##### Abstract:

We investigate some structural properties of C*-algebras generated by quasi-regular representations of stabilizers of boundary actions of discrete groups G. Our main tool is the notion of (noncommutative) boundary maps, namely G-equivariant unital positive maps from G-C*algebras to C(B), where B is the Furstenberg boundary of G. We completely describe the tracial structure and characterize the simplicity of these C*-algebras. As an application, we show that the C*-algebra generated by the quasi-regular representation associated to Thompson's groups $F < T$ does not admit traces and is simple. \\ \\ This is joint work with Eduardo Scarparo.

Host: Matthew Wiersma

### February 23, 2021

### 10:00 AM

### Contact mtwiersma@ucsd.edu

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