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# Operator Algebra and Noncommutative Geometry Seminar Series

## July 25, 2019 @ 3:30 pm - 4:30 pm

##### Speaker

Dr James Gabe (UOW)

##### Title

Lifting KK-elements to *-homomorphisms.

##### Abstract

Let A be a separable, nuclear C*-algebra, and B be a unital, properly infinite C*-algebra. I will outline how to lift any element in KK(A,B) to an injective *-homomorphism. This is the “existence part” of my new proof of the Kirchberg-Phillips theorem. The main new ingredient is the (very elementary) construction of a unitary path with magical properties.