The descriptive set theory of C$^*$-algebra invariants
The descriptive set theory of C$^*$-algebra invariants
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C$^*$-代数不变量的描述性集合论
DOI：
10.1093/imrn/rns206
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Asger Tornquist
中科院分区：
文献类型：
--
作者：
I. Farah;Andrew S. Toms;Asger Tornquist
我们建立了各种C$^*$-代数不变量的Borel可计算性，包括Elliott不变量和Cuntz半群。作为应用，我们推导出AF代数是可分类的可数结构，和猜测的冬天和第二作者的核可分简单C*-代数不能反驳呼吁这些代数的标准Borel结构。
We establish the Borel computability of various C$^*$-algebra invariants, including the Elliott invariant and the Cuntz semigroup. As applications we deduce that AF algebras are classifiable by countable structures, and that a conjecture of Winter and the second author for nuclear separable simple C*-algebras cannot be disproved by appealing to known standard Borel structures on these algebras.