Classification of ${\mathcal{O}}_{\infty }$-stable $C^{\ast }$-algebras

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.

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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Cited by in corpus (3)

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• Spanier-Whitehead K-Duality and Duality of Extensions of $C^{\ast }$-algebras