Classification of $\mathcal O_\infty$-stable $C^\ast$-algebras

James Gabe

Classification of $\mathcal O_\infty$-stable $C^\ast$-algebras

Operator Algebras 2021-07-01 v3 K-Theory and Homology

Authors: James Gabe

Abstract

I present a proof of Kirchberg's classification theorem: two separable, nuclear, $\mathcal O_\infty$ -stable $C^\ast$ -algebras are stably isomorphic if and only if they are ideal-related $KK$ -equivalent. In particular, this provides a more elementary proof of the Kirchberg--Phillips theorem which is isolated in the paper to increase readability of this important special case.

Keywords

cuntz semigroup c*-algebras graph algebras

Cite

@article{arxiv.1910.06504,
  title  = {Classification of $\mathcal O_\infty$-stable $C^\ast$-algebras},
  author = {James Gabe},
  journal= {arXiv preprint arXiv:1910.06504},
  year   = {2021}
}

Comments

To appear in Mem. Amer. Math. Soc., 112 pages, v3 (accepted version): added two subsections (8.4 and 15.3) on approximate equivalence. v2: minor changes

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