A new proof of Kirchberg's \mathcal O₂-stable classification

2017/06/12 by James Gabe, Gabe, James · 3 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1706.03690

openalex publication_date 2017/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I present a new proof of Kirchberg's \mathcal O₂-stable classification theorem: two separable, nuclear, stable/unital, \mathcal O₂-stable C^∗-algebras are isomorphic if and only if their ideal lattices are order isomorphic, or equivalently, their primitive ideal spaces are homeomorphic. Many intermediate results do not depend on pure infiniteness of any sort.

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• Decomposing nuclear maps
• The nuclear dimension of \mathcal O_∞-stable C^*-algebras
• Rohlin actions of finite groups on the Razak-Jacelon algebra

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