تقرير
A type I conjecture and boundary representations of hyperbolic groups
| العنوان: | A type I conjecture and boundary representations of hyperbolic groups |
|---|---|
| المؤلفون: | Caprace, Pierre-Emmanuel, Kalantar, Mehrdad, Monod, Nicolas |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, Mathematics - Dynamical Systems, Mathematics - Operator Algebras |
| الوصف: | We establish new results on the weak containment of quasi-regular and Koopman representations of a second countable locally compact group $G$ associated with non-singular $G$-spaces. We deduce that any two boundary representations of a hyperbolic locally compact group are weakly equivalent. We also show that non-amenable hyperbolic locally compact groups with a cocompact amenable subgroup are characterized by the property that any two proper length functions are homothetic up to an additive constant. Combining those results with the work of \L. Garncarek on the irreducibility of boundary representations of discrete hyperbolic groups, we deduce that a type I hyperbolic group with a cocompact lattice contains a cocompact amenable subgroup. Specializing to groups acting on trees, we answer a question of C. Houdayer and S. Raum. Comment: Amendments to Theorem G and Corollary H; new Proposition 3.2; minor changes to improve the exposition |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2110.00190 |
| رقم الأكسشن: | edsarx.2110.00190 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |