Rigidity results for group von Neumann algebras with diffuse center


We introduce the first examples of groups G with infinite center which in a natural sense are recognizable from their von Neumann algebras, L(G). Specifically, assume that G = A x G_0, where A is an infinite abelian group and G_0 is an ICC wreath-like product group with property (T), trivial abelianization and torsion free outer automorphism group. 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 G_0. 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.


ASUERAU C*-Seminar
October 26, 2023

Virtual via Zoom
3:00 - 4:00pm MST/AZ

The seminar is organized jointly with Mitch Hamidi and Lara Ismert at Embry-Riddle Aeronautical University in Prescott, AZ.

(Please email the organizers Steve Kaliszewski and Jack Spielberg to be put on the email list if you would like to receive the link to the zoom seminar.)


Adriana Fernandez I Quero
University of Iowa
(presenting via Zoom)

Virtual via Zoom