当前位置: X-MOL 学术Isr. J. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
The Calkin algebra is ℵ1-universal
Israel Journal of Mathematics ( IF 1 ) Pub Date : 2020-05-14 , DOI: 10.1007/s11856-020-2007-y
Ilijas Farah , Ilan Hirshberg , Alessandro Vignati

We discuss the existence of (injectively) universal C*-algebras and prove that all C*-algebras of density character ℵ1 embed into the Calkin algebra, Q(H). Together with other results, this shows that each of the following assertions is relatively consistent with ZFC: (i) Q(H) is a 2ℵ0-universal C*-algebra. (ii) There exists a 2ℵ0-universal C*-algebra, but Q(H) is not 2ℵ0-universal, (iii) A 2ℵ0-universal C*-algebra does not exist. We also prove that it is relatively consistent with ZFC that (iv) there is no ℵ1-universal nuclear C*-algebra, and that (v) there is no ℵ1-universal simple nuclear C*-algebra.

中文翻译:

Calkin 代数是 ℵ1-普遍的

我们讨论了(注入式)通用 C*-代数的存在,并证明了所有密度特征为 ℵ1 的 C*-代数都嵌入到 Calkin 代数 Q(H) 中。连同其他结果,这表明以下每个断言都与 ZFC 相对一致: (i) Q(H) 是一个 2ℵ0-通用 C*-代数。(ii) 存在一个 2ℵ0-universal C*-代数,但 Q(H) 不是 2ℵ0-universal,(iii) 一个 2ℵ0-universal C*-代数不存在。我们还证明了与ZFC相对一致的是(iv)不存在ℵ1-普遍核C*-代数,并且(v)不存在ℵ1-普遍简单核C*-代数。
更新日期:2020-05-14
down
wechat
bug