Classifying $^*$-homomorphisms I: Unital simple nuclear $C^*$-algebras

By Jos'e R. Carri'on, James Gabe, Christopher Schafhauser, Aaron Tikuisis, Stuart White. 2023

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We classify the unital embeddings of a unital separable nuclear $C^*$-algebra satisfying the universal coefficient theorem into a unital simple separable nuclear $C^*$-algebra that tensorially absorbs the Jiang--Su algebra. This gives a new and essentially self-contained proof of the stably finite case of the unital classification theorem: unital simple separable nuclear $C^*$-algebras that absorb the Jiang--Su algebra tensorially and satisfy the universal coefficient theorem are classified by Elliott's invariant of $K$-theory and traces.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/574cc54d2e428951892042c9fd2aa01a7c9bde8a