PreprintarXiv licencearXiv
ICC property (T) groups without W*-superrigidity
Abstract
We construct two explicit countable discrete groups Γ1 and Γ2 that are both ICC and have Kazhdan's property (T). Although Γ1 and Γ2 are not isomorphic as groups, their group von Neumann algebras are isomorphic: L(Γ1)≅ L(Γ2). 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.
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BibTeX
@misc{zhou2026property,
title = {{ICC property (T) groups without W$^*$-superrigidity}},
author = {Shuoxing Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.02327},
eprint = {2608.02327},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.02327},
}
RIS
TY - UNPB
TI - ICC property (T) groups without W^*-superrigidity
AU - Shuoxing Zhou
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2608.02327
UR - https://arxiv.org/abs/2608.02327
AB - We construct two explicit countable discrete groups Γ_1 and Γ_2 that are both ICC and have Kazhdan's property (T). Although Γ_1 and Γ_2 are not isomorphic as groups, their group von Neumann algebras are isomorphic: L(Γ_1)≅ L(Γ_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.
ER -