ICC property(T) groups without W${}^{\ast }$-superrigidity

Abstract

We construct two explicit countable discrete groups $\hat{I}{“}_1$ and $\hat{I}{“}_2$ that are both ICC and have Kazhdan's property (T). Although $\hat{I}{“}_1$ and $\hat{I}{“}_2$ are not isomorphic as groups, their group von Neumann algebras are isomorphic: $L(\hat{I}{“}_1)\cong L(\hat{I}{“}_2)$. This provides a counterexample to Connes' rigidity conjecture for ICC property (T) groups. This result was obtained with assistance from GPT-5.6 Sol, independently of and concurrently with work by OpenAI.

21 pages