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

#### Adriana Fernandez I Quero; University of Iowa

We introduce the first examples of groups with infinite center which in a natural sense are recognizable from their von Neumann algebras. Specifically, assume that G=A\times W, where A is an infinite abelian group and W 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 \mathcal{L}(G) is *-isomorphic to \mathcal L(H), it must be the case that H= B \times W where B is infinite abelian. Moreover, we completely describe the *-isomorphism between the two group von Neumann algebras. 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.