Almost elementary groupoids and classifiable C*-algebras

Jianchao Wu  (Shanghai Center for Mathematical Sciences)

10:00-11:00£¨April10£¨2024    ScienceBuilding A503




Abstract:

This talk is based on collaborations with Xin Ma, where we introduce and study a notion of almost elementary ®¶tale groupoids as a dynamic analog of (tracial) Z-stability. In particular, the reduced groupoid C*-algebra of an almost elementary minimal ®¶tale groupoid (e.g., the reduced crossed product associated to an almost elementary minimal action by a discrete group) is tracially Z-stable. To further corroborate the this analogy, we recently showed that many classifiable C*-algebras (including all of the strongly self-absorbing ones) have almost elementary ®¶tale groupoid models. It appears necessary to work in the generality of groupoids rather than just group actions: we also present a result that demonstrate the difficulty of constructing a crossed product model for the Jiang-Su algebra Z.

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