Almost elementary groupoids and their C*-algebras

Xin Ma

*(York University)*

11:00-12:00£¬ August 1£¬2024 Tian Jiabing Building 323

__Abstract:__

In this talk, I will present new results on almost
elementariness, which was introduced as a new finite approximation
property for locally compact Hausdorff \'{e}tale groupoids and implies
the (tracial) Z-stability for groupoid C*-algebras. I will demonstrate
that for a large class C of Elliott invariants and for any unital
C*-algebra A whose Elliott invariant Ell(A) in C, the C*-algebra A is
classifiable if and only if A has an almost elementary groupoid model.
As an application, every strongly self-absorbing C*-algebra satisfying
the UCT has an almost elementary groupoid model. This is based on a
joint work with Jianchao Wu.

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