Rigid sides of approximately finite dimensional simple operator algebras in non-separable category
Rigid sides of approximately finite dimensional simple operator algebras in non-separable category
复制标题
不可分范畴中近似有限维简单算子代数的刚性边
DOI：
10.1093/imrn/rnz079
复制
发表时间：
2019
影响因子：
1
通讯作者：
Yuhei Suzuki
中科院分区：
文献类型：
--
作者：
Siwattra Choodej，Khanitha Pudhom，Kosei Yamauchi;Tohru Mitsunaga;Yuhei Suzuki
应用波帕的正交性方法的一类新的群体，我们构造顺从的群因子是素的，没有无限维正则阿贝尔子代数。通过将Dixtons问题的Farah-Katalah解调整到von Neumann代数的背景下，得到了素近似有限维因子和张素单AF-代数的第1个例子.我们的结果证明了Zermelo-Fraenkel集理论与公理的选择（ZFC），从而特别回答了法拉-海瑟薇-Katsura-Tikuisis提出的问题。我们还直接确定某些交叉产品的中心序列。这就说明了在不可分情形下Kirchberg吸收定理的失败。
Applying Popa’s orthogonality method to a new class of groups, we construct amenable group factors that are prime and have no infinite-dimensional regular abelian-subalgebras. By adjusting Farah–Katsura’s solution of Dixmier’s problem to the von Neumann algebra setting, we obtain the 1st examples of prime approximately finite-dimensional factors and tensorially prime simple AF-algebras. Our results are proved in Zermelo--Fraenkel set theory with the axiom of choice (ZFC), thus in particular answering questions asked by Farah–Hathaway–Katsura–Tikuisis. We also directly determine central sequences of certain crossed products. This concludes the failure of the Kirchberg-absorption theorem in the non-separable setting.