Almost elementary groupoids and their C*-algebras

Xin Ma  (York University)

11:00-12:00úČ August 1úČ2024    Tian Jiabing Building 323


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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