A new proof of Kirchberg's 𝒪2-stable classification-Reference-Cited by-同舟云学术

A new proof of Kirchberg's 𝒪2-stable classification

Published:2018-05-16 Issue:761 Volume:2020 Page:247-289
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Gabe James¹^ORCID

Affiliation:

1. Mathematical Sciences, University of Southampton, SO17 1BJ, United Kingdom . Current address: School of Mathematics and Statistics , University of Glasgow , University Place , Glasgow G12 8SQ , Scotland , United Kingdom

Abstract

Abstract I present a new proof of Kirchberg’s 𝒪 2

\mathcal{O}_{2}

-stable classification theorem: two separable, nuclear, stable/unital, 𝒪 2

\mathcal{O}_{2}

-stable C ∗

C^{\ast}

-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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2018-0010/pdf

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