Classification of \mathcal O_∞-stable C^∗-algebras

2019/10/15 by Gabe, James
#46L35 #46L80 #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1910.06504

Abstract

I present a proof of Kirchberg's classification theorem: two separable, nuclear, \mathcal O_∞-stable C^∗-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.

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