Classification of non-simple purely infinite C*-algebras

非简单纯无限 C* 代数的分类

• 批准号: 270818892
• 负责人: Professor Dr. Ralf Meyer
• 金额: --
• 依托单位: Mathematisches Institut (MI)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/270818892?language=en
• 关键词: Classification; non; simple; purely; infinite

Certain classes of C*-algebras may be classified by simple invariants. This is well-known for purely infinite, nuclear, separable, simple C*-algebras. Allowing non-simple C*-algebras adds a new topological complexity to the classification problem, which is not yet understood in general. In many case, a newly found invariant gives complete classification results. In particular, this new invariant gives a strong classification theorem for graph C*-algebras and for C*-algebras over finite spaces whose Hasse diagram is a quiver. This project will further develop this approach to classification of non-simple C*-algebras.In particular, we want to find out which values the invariant may take on graph C*-algebras, how and with what data to compute the invariant explicitly, and how to extend the classification result to other classes of examples. For graph C*-algebras, we want to implement a computer algorithm that decides whether two graph C*-algebras are isomorphic using the invariant. The invariant also hints at how to enlarge the class of graph C*-algebras without losing too much of their nice structure. These hints shall be followed to find more general models for classifiable purely infinite C*-algebras.

某些类的C*-代数可以用简单不变量来分类。这是众所周知的纯无限，核，可分，简单的C*-代数。允许非单C*-代数给分类问题增加了新的拓扑复杂性，这还没有被普遍理解。 在许多情况下，新发现的不变量会给出完整的分类结果。特别地，这个新的不变量给出了图C*-代数和Hasse图为图的有限空间上的C*-代数的一个强分类定理。本项目将进一步发展这种方法来分类非简单C*-代数，特别是，我们想知道图C*-代数上的不变量可以取哪些值，如何以及用什么数据显式计算不变量，以及如何将分类结果扩展到其他类别的例子。对于图C*-代数，我们希望实现一个计算机算法，利用不变量判定两个图C*-代数是否同构。这个不变量也暗示了如何扩大图C*-代数的类，而不会失去太多它们的漂亮结构。这些提示将被用来寻找可分类的纯无限C*-代数的更一般的模型。

项目成果

Cuntz Splice invariance for purely infinite graph algebras

纯无限图代数的 Cuntz 拼接不变性

• DOI: 10.7146/math.scand.a-96633
• 发表时间: 2018
• 期刊: arXiv: Operator Algebras
• 作者: Rasmus Bentmann