Classification of 𝒪_{∞}-Stable 𝒞*-Algebras

Abstract

I present a proof of Kirchberg’s classification theorem: two separable, nuclear, O ∞ \mathcal O_\infty -stable C ∗ C^\ast -algebras are stably isomorphic if and only if they are ideal-related K K 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.