Recovering the Elliott invariant from the Cuntz semigroup
Recovering the Elliott invariant from the Cuntz semigroup
复制标题
从 Cuntz 半群恢复艾略特不变量
DOI：
10.1090/s0002-9947-2014-05833-9
复制
发表时间：
2011
影响因子：
1.3
通讯作者：
Luis Santiago
中科院分区：
文献类型：
--
作者：
Ramon Antoine;M. Dadarlat;F. Perera;Luis Santiago
设A是稳定秩为1的单可分C-代数.证明了C（T，A）的Cuntz半群由其投影的Murray-von Neumann半群和某个下连续函数半群（其值在A的Cuntz半群中）所决定.这一结果有两个后果。首先，专门针对A是简单的、有限的、可分的和Z-稳定的情形，这就给出了C（T，A）的Cuntz半群的Elliott不变量的描述。其次，通过适当的解释，证明了Elliott函子与由张量积的Cuntz半群与圆上连续函数代数所定义的函子是自然等价的。
Let A be a simple, separable C � -algebra of stable rank one. We prove that the Cuntz semigroup of C(T,A) is determined by its Murray-von Neumann semigroup of projections and a certain semigroup of lower semicontinuous functions (with values in the Cuntz semigroup of A). This result has two consequences. First, specializing to the case that A is simple, finite, separable and Z-stable, this yields a description of the Cuntz semigroup of C(T,A) in terms of the Elliott invariant of A. Second, suitably interpreted, it shows that the Elliott functor and the functor de- fined by the Cuntz semigroup of the tensor product with the algebra of continuous functions on the circle are naturally equivalent.