相对双曲群的相对双精确性及其若干应用
Relative Biexactness for Relative Hyperbolic Groups and Some Applications
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中文总结 AI 辅助
本文证实Ozawa等人关于有限生成相对双曲精确群为相对双精确的猜想，由此得到素群冯·诺依曼代数，并构造了两两非稳定*同构的群测度空间冯·诺依曼代数族。
中文摘要 AI 辅助
本文证实了Ozawa等人提出的猜想，即每个有限生成的相对双曲精确群，在其自然外围结构下是相对双精确的（按Ozawa的定义）。由此，每个此类群都对应一个素群冯·诺依曼代数。作为应用，我们构造了具有性质(T)的相对双曲群的连续族{G_i}_{i∈I}，使得对任意固定的自由、遍历、保概率测度作用G_i ↷ Z_i，对应的群测度空间冯·诺依曼代数族{L^∞(Z_i) ⋊ G_i}_{i∈I}两两非稳定*同构。
英文摘要
In this paper, we confirm a conjecture of Ozawa and others asserting that every finitely generated, relatively hyperbolic, exact group is bi-exact (in the sense of Ozawa) relative to its natural peripheral structure. As a consequence, every such group gives rise to a prime group von Neumann algebra. As an application, we construct a continuum family of property (T), relatively hyperbolic groups $\{G_i\}_{i\in I}$ such that, for every fixed arbitrary free, ergodic, probability measure-preserving action $G_i \curvearrowright Z_i$, the collection of associated group measure space von Neumann algebras $\{L^\infty(Z_i)\rtimes G_i\}_{i\in I}$ are pairwise non-stably $\ast$-isomorphic.
