Classification of C*-algebras real rank zero and stable rank one

Qingnan An  (Northeast Normal University)

16:00-17:00£¨July 30th£¨2024    Tian Jiabing Building 323


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. 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.

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