An operator algebras seminar at SIMIS: Classification of C*-algebras real rank zero and stable rank one

Speaker：Qingnan An

Host: Huaxin Lin

Abstract: We will talk about the Elliott conjecture of real rank zero setting which would briefly involve Total K-theory, Universal Multi-Coefficient Theorem, Bockstein Operations and a new invariant called Total Cuntz semigroup. By considering the the classification of extensions of C*-algebras, we exhibit two unital, separable, nuclear C*-algebras of stable rank one and real rank zero with the same ordered scaled total K-theory satisfying UCT, but they are not isomorphic with each other, which forms a counterexample to Elliott Classification Conjecture for real rank zero setting. We point out that such a result reveals the necessity of the orders from the Total K-theory of ideals. Moreover, we will also show that the Coefficient maps from the Total K-theory of ideals are also indispensable, while the Bockstein Operations are automatic. This serry of works are jointed with Zhichao Liu.

Time: 14:30, Thursday, September 12, 2024

Location: Room 1510, Block A, No. 657 Songhu Road, Yangpu District, Shanghai

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报搞人简介：安庆楠，东北师范大学数学与统计学院分析方向讲师，主要主要研究兴趣是C*-代数的分类与不变量等相关理论，部分科研成果在Proc. Lond. Math. Soc.、J. Funct. Anal.、J. Operator Theory、Sci. China Math.等期刊发表。2023年度，入选天元东北中心优秀青年学者。