##### Department of Mathematics,

University of California San Diego

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### Math 243, Functional Analysis

## Adriana Fernandez I Quero

#### The University of Iowa

## Rigidity results for group von Neumann algebras with diffuse center

##### Abstract:

We introduce the first examples of groups G with an infinite center which in a natural sense are completely recognizable from their von Neumann algebras, L(G). Specifically, assume that G=A x W, where A is an infinite abelian group and W is an ICC wreath-like product group with property (T) and trivial abelianization. Then whenever H is an arbitrary group such that L(G) is isomorphic to L(H), via an arbitrary isomorphism preserving the canonical traces, it must be the case that H= B x H_0 where B is infinite abelian and H_0 is isomorphic to W. Moreover, we completely describe the isomorphism between L(G) and L(H). This yields new applications to the classification of group C*-algebras, including examples of non-amenable groups which are recoverable from their reduced C*-algebras but not from their von Neumann algebras. This is joint work with Ionuţ Chifan and Hui Tan.

Host:
Priyanga Ganesan

### February 13, 2024

### 11:00 AM

APM 5829 and** **Zoom (meeting ID: 94246284235)

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