Event ·Official first-hand

ICC性质T群不满足W$^*$-超刚性：Connes刚性猜想反例

arXiv论文构造了两个可数离散群Γ1和Γ2，二者均为ICC群且具有Kazhdan性质(T)，但两群不同构。它们的群von Neumann代数却同构，即L(Γ1)≅L(Γ2)。该结果构成Connes刚性猜想在ICC性质(T)群情形下的反例。论文注明该结果由GPT-5.6 Sol辅助获得，并与OpenAI的工作独立且同时完成。

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论文给出了Connes刚性猜想的具体反例，两个不同构的ICC性质T群居然有同构的群von Neumann代数，搞算子代数的人值得一看。

6 sources42° AI heatLast updated 2026/8/3 14:50:28

Evidence

6 sources

Primary sourcearXiv: OpenAI

2026/8/3 14:50:28View source

Related source 1elvis

2026/8/1 16:41:45View source

Related source 2Gary Marcus

2026/8/1 14:59:48View source

Related source 3歸藏(guizang.ai)

2026/8/1 15:44:06View source

Related source 4OpenAI

2026/8/3 18:54:16View source

Related source 5量子位

2026/8/4 09:22:46View source

Conflict check

Dedup data only shows that these sources discuss the same event, not that they agree. There is no structured supporting or refuting evidence yet, so no conflict is inferred automatically.

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