The classification of real purely infinite simple C*-algebras
The classification of real purely infinite simple C*-algebras
复制标题
实纯无穷简单C*代数的分类
DOI：
10.4171/dm/345
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发表时间：
2011
影响因子：
0.9
通讯作者：
P. Stacey
中科院分区：
文献类型：
--
作者：
Jeffrey L. Boersema;Efren Ruiz;P. Stacey
利用统一K理论对真实的基希贝格代数进行了分类.确切地说，设A和B是满足泛系数定理的真实的单可分核纯无限C*-代数，使得AC和BC也是单的。在稳定情形下，A和B同构当且仅当K（A）= K（B）。在酉情形下，A和B同构当且仅当（K（A），[1A]）n =（K（B），[1 B]）.我们还证明了这样一个真实的C*-代数的复化是纯无限的，解决了[43]中的一个问题。因此，这里所分类的真实的C*-代数就是复化福尔斯属于基希贝格[26]和菲利普斯[35]分类结果的那些真实的C*-代数。作为应用，我们求出了复Cuntz代数On（2 ≤ n ≤ ∞）的所有真实的形式. 2010年数学学科分类：46 L35、46 L 80、19 K99
We classify real Kirchberg algebras using united Ktheory. Precisely, let A and B be real simple separable nuclear purely infinite C*-algebras that satisfy the universal coefficient theorem such that AC and BC are also simple. In the stable case, A and B are isomorphic if and only if K(A) ∼= K(B). In the unital case, A and B are isomorphic if and only if (K (A), [1A]) ∼= (K(B), [1B]). We also prove that the complexification of such a real C*-algebra is purely infinite, resolving a question left open from [43]. Thus the real C*-algebras classified here are exactly those real C*-algebras whose complexification falls under the classification result of Kirchberg [26] and Phillips [35]. As an application, we find all real forms of the complex Cuntz algebras On for 2 ≤ n ≤ ∞. 2010 Mathematics Subject Classification: 46L35, 46L80, 19K99