A new proof of Kirchberg's $\mathcal O_2$-stable classification
Operator Algebras
2018-04-10 v2
Abstract
I present a new proof of Kirchberg's -stable classification theorem: two separable, nuclear, stable/unital, -stable -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.
Keywords
Cite
@article{arxiv.1706.03690,
title = {A new proof of Kirchberg's $\mathcal O_2$-stable classification},
author = {James Gabe},
journal= {arXiv preprint arXiv:1706.03690},
year = {2018}
}
Comments
Final version, to appear in J. Reine Angew. Math., 39 pages