由类Thompson群产生的McDuff与素von Neumann代数
算子代数
2024-10-04 v3 动力系统
群论
摘要
在本文中，我们证明了Skipper和Zaremsky [SZ21]的克隆系统构造，在充分条件下，会产生稳定的类Thompson群；特别地，这些群是Deprez和Vaes [DV18]意义下的McDuff群。这正面回答了Bashwinger和Zaremsky在[BZ23]中提出的一个问题。在相反的方向上，我们证明了Higman-Thompson群和的群von Neumann代数都是素II因子。这源于对某一类群的一个新的形变/刚性论证，该类群允许一个到拟正则表示的真上循环，而该表示不一定是弱的。
引用
@article{arxiv.2312.08345,
title = {McDuff and Prime von Neumann algebras arising from Thompson-Like Groups},
author = {Rolando de Santiago and Patrick DeBonis and Krishnendu Khan},
journal= {arXiv preprint arXiv:2312.08345},
year = {2024}
}
备注
Groups action on trees removed. Fix the proof Theorem 4.5 which is now Theorem 4.10. Removed an assumption from Theorem A (Theorem 3.3). Fixed the proof of Theorem D/corollary 6.5 (now Theorem C/corollary 5.11). Removed Theorem C. Fix Theorem 4.5 (now Theorem 4.10). Combined section 5 and 6. Corrected the proof of lemma 6.1 (now lemma 5.6). Corrected the proof of lemma 6.1 (now lemma 5.6)