论文标题
von Neumann代数的半领产品刚度是由$ \ Mathscr {s} $，归纳限制和基本组引起的
Semidirect product rigidity of group von Neumann algebras arising from class $\mathscr{S}$, inductive limits and fundamental group
论文作者
论文摘要
在本文中，我们研究了\ cite {cdk19}的几何群体理论中撕裂构建的属性（t）组，以及该类别的某些归纳极限组。使用Popa的变形/刚度与几何组理论中的方法之间的相互作用，我们能够扩展\ cite {cdk19}中考虑的组类别，这些组在传递到von neumann代数的同时纪念半领产品特征。将这些结果与在\ cite {cdhk20}中开发的方法相结合，我们能够通过琐碎的基本组生成更多的属性（t）组因子示例。归纳极限组没有属性（t），并提供了琐碎基本组的更多因素的例子。我们还能够显示这些群体的cartan刚度。
In this article we study property (T) groups arising from Rips construction in geometric group theory in the spirit of \cite{CDK19} and certain inductive limit groups from this class. Using interplay between Popa's deformation/rigidity and methods in geometric group theory we are able to extend the class of groups considered in \cite{CDK19} that remembers semidirect product features while passing to the group von Neumann algebras. Combining these results with the method developed in \cite{CDHK20} we are able to produce more examples of property (T) group factors with trivial fundamental group. The inductive limit groups do not have property (T) and provides examples of more factors with trivial fundamental group. We are also able to show Cartan rigidity for these groups.
