Operator Theory Seminar

Speaker: 
Adriana Fernandez Quero
Topic: 
Rigidity results for group von Neumann algebras with diffuse center

Abstract:

We introduce the first examples of groups G with 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 Ionut Chifan and Hui Tan.

 

 

UICapture link to recordings:

https://uicapture.hosted.panopto.com/Panopto/Pages/Sessions/List.aspx?folderID=75895471-c576-404c-805f-af6d013f81d3

Event Date: 
February 6, 2024 - 1:30pm to 2:30pm
Location: 
VAN 309 or Online (See URL)
Calendar Category: 
Seminar
Seminar Category: 
Operator Theory