College of Liberal Arts & Sciences

# Operator Theory Seminar

**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.

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