تقرير
Wreath-like products of groups and their von Neumann algebras I: $W^\ast$-superrigidity
| العنوان: | Wreath-like products of groups and their von Neumann algebras I: $W^\ast$-superrigidity |
|---|---|
| المؤلفون: | Chifan, Ionut, Ioana, Adrian, Osin, Denis, Sun, Bin |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Operator Algebras, Mathematics - Dynamical Systems, Mathematics - Functional Analysis, Mathematics - Group Theory |
| الوصف: | We introduce a new class of groups called wreath-like products. These groups are close relatives of the classical wreath products and arise naturally in the context of group theoretic Dehn filling. Unlike ordinary wreath products, many wreath-like products have Kazhdan's property (T). In this paper, we prove that any group $G$ in a natural family of wreath-like products with property (T) is W$^*$-superrigid: the group von Neumann algebra $\text{L}(G)$ remembers the isomorphism class of $G$. This allows us to provide the first examples (in fact, $2^{\aleph_0}$ pairwise non-isomorphic examples) of W$^*$-superrigid groups with property (T). Comment: The original paper (v1) has been split into three papers; results are strengthened and proofs are simplified. This is the first paper in the series, which contains results on W*-superrigidity. The second and third papers will focus on outer automorphisms and embeddings of von Neumann algebras of wreath-like products, respectively. To appear in the Annals of Mathematics |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2111.04708 |
| رقم الأكسشن: | edsarx.2111.04708 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |