The classification problem for separable amenable simple C*-algebras

George Elliott

*(University of Toronto)*

8:15-9:15£¬July 29£¬2024 Online

__Abstract:__

For Jiang-Su stable separable amenable simple C*-algebras satisfying the UCT, the naive invariant consisting, in the stable case, of the even and odd K-groups (arbitrary countable abelian groups), together with the cone of traces (an arbitrary cone with a metrizable Choquet simplex - not an invariant - as base), and the natural pairing (arbitrary) of this cone with the even K-group, is a strong classification functor. (See the ICBS Frontiers of Science survey article by Gong, Lin, and Niu.)
The even K-group, paired with the tracial cone, in the finite Jiang-Su stable case exactly constitutes the Cuntz semigroup, which suggests replacing it with this ordered semigroup when the algebra is no longer Jiang-Su stable. There are interesting cases in which this suffices. (Beginning with work of C.G. Li, Niu, and me to appear in JFA.)

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