The classification of non-classifiable simple C*-algebras---a beginning

George Elliott  (University of Toronto)

9:05-10:05,July 31,2023   Online: Zoom Meeting ID: 336 111 4671 Passcode: RCOA2023

Abstract:

The class of what are at present referred to as classifiable simple C*-algebras is extended in recent joint work with Chun Guang Li and Zhuang Niu to include all Villadsen algebras of the first kind with seed spaces cubes of finite dimension. As for previous extensions of the classifiable class (e.g., passing from AF algebras to AI algebras), this extension requires an enlargement of the invariant---now to include the Cuntz semigroup, which turns out to be determined by the Elliott invariant (as it was in the earlier setting) together with, in addition, the Toms radius of comparison. (This can be any positive real number or infinity.)

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