تقرير
Rigidity results for group von Neumann algebras with diffuse center
| العنوان: | Rigidity results for group von Neumann algebras with diffuse center |
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| المؤلفون: | Chifan, Ionuţ, Quero, Adriana Fernández, Tan, Hui |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Operator Algebras |
| الوصف: | We introduce the first examples of groups $G$ with infinite center which in a natural sense are completely recognizable from their von Neumann algebras, $\mathcal{L}(G)$. Specifically, assume that $G=A\times W$, where $A$ is an infinite abelian group and $W$ is an ICC wreath-like product group [CIOS22a; AMCOS23] with property (T) and trivial abelianization. Then whenever $H$ is an \emph{arbitrary} group such that $\mathcal{L}(G)$ is $\ast$-isomorphic to $\mathcal L(H)$, via an \emph{arbitrary} $\ast$-isomorphism preserving the canonical traces, it must be the case that $H= B \times H_0$ where $B$ is infinite abelian and $H_0$ is isomorphic to $W$. Moreover, we completely describe the $\ast$-isomorphism between $\mathcal L(G)$ and $\mathcal L(H)$. 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. Comment: After the first version was posted, Stefaan Vaes pointed out one of the equivalences in Theorem 4.5 does not hold as stated. In the current version we fixed this along with the proofs where it was used. This does not affect the main result or the substance of the arguments used. The only difference is that now Corollary D is slightly more restrictive. We also corrected a number of typos |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.01280 |
| رقم الأكسشن: | edsarx.2403.01280 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |