algebra / Operator algebras
Connes' rigidity conjecture asks whether an ICC group with Kazhdan's property (T) is determined by its group von Neumann algebra. Disproved for this class: two explicit countable discrete groups $\Gamma_1$ and $\Gamma_2$, both ICC and property (T), are non-isomorphic as groups while $L(\Gamma_1) \cong L(\Gamma_2)$.
Temporal state
No reconciled state yet.
Append-only history
Settles the ICC property (T) case. The paper records that the result was obtained independently of and concurrently with work by OpenAI.
Research memory
Connes' rigidity conjecture asks whether an ICC group with Kazhdan's property (T) is determined by its group von Neumann algebra. Disproved for this class: two explicit countable discrete groups $\Gamma_1$ and $\Gamma_2$, both ICC and property (T), are non-isomorphic as groups while $L(\Gamma_1) \cong L(\Gamma_2)$.
Settles the ICC property (T) case. The paper records that the result was obtained independently of and concurrently with work by OpenAI.
Evidence graph
generalizes · problem · claimed