A latticed total K-theory

Qingnan An 安庆楠

*(Northeast Normal University)*

10:00-11:00, September 11, 2024 Science Building A503

__Abstract:__

The K_0(A) group of a unital C*-algebra A is obtained as the Grothendick group of V(A). It is well know that, if V(A) has cancellation (or A has stable rank one), then V(A) coincides with the positive cone in K_0^+(A) in K_0(A). But if V(A) doesn’t has cancellation, we would lost some information from the Grothendick procedure. We will talk about an analogue of V(A), which we called the latticed total K-theory V(A). We show that V(A) plays a similar role for the total K-theory K(A) and there exist two non-isomorphic unital, separable, nuclear C*-algebras of stable rank one and real rank zero with the same ordered scaled total K-theory satisfying UCT, but the invariant V distinguishes them. That is, the information we lost in the Grothendick procedure is necessary for the classification. Our discussion will also contain some refinement of Cuntz semigroup, the Bockstein Operations and UCT. The talk will be based on joint works with Chunguang Li and Zhichao Liu.

__About the speaker:__

安庆楠，东北师范大学数学与统计学院分析方向讲师，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。

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