A unified approach for classifying simple nuclear C^∗-algebras

2024/12/20 by Ben Bouwen, Bouwen, Ben, James Gabe +1
Mathematics · #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2412.15968

Abstract

We provide a new proof of the Kirchberg--Phillips theorem by adapting the framework laid out by Carrión--Gabe--Schafhauser--Tikuisis--White for classifying separable simple unital nuclear stably finite \mathcal Z-stable C^∗-algebras satisfying the UCT. Not only does this give a unified approach to classifying stably finite and purely infinite C^∗-algebras, in contrast to the other proofs of the Kirchberg--Phillips theorem, our proof does not rely on Kirchberg's Geneva Theorems, but instead implies them as corollaries (for nuclear C^∗-algebras).

Related

• Classification of \mathcal O_∞-stable C^∗-algebras
• The UCT problem for nuclear C^∗-algebras
• Nuclear dimension and Z-stability of pure C*-algebras
• Classifying ^*-homomorphisms I: Unital simple nuclear C^*-algebras
• A new proof of Kirchberg's \mathcal O₂-stable classification