Journal of Noncommutative Geometry

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Volume 8, Issue 4, 2014, pp. 1061–1081
DOI: 10.4171/JNCG/178

Published online: 2015-02-02

Kirchberg $X$-algebras with real rank zero and intermediate cancellation

Rasmus Bentmann[1]

(1) Georg-August Universität Göttingen, Germany

A universal coecient theorem is proved for $C*$-algebras over an arbitrary finite $T_0$-space $X$ which have vanishing boundary maps. Under bootstrap assumptions, this leads to a complete classification of unital/stable real-rank-zero Kirchberg $X$-algebras with intermediate cancellation. Range results are obtained for (unital) purely infinite graph $C*$-algebras with intermediate cancellation and Cuntz–Krieger algebras with intermediate cancellation. Permanence results for extensions of these classes follow.

Keywords: Kirchberg algebras, K-theory

Bentmann Rasmus: Kirchberg $X$-algebras with real rank zero and intermediate cancellation. J. Noncommut. Geom. 8 (2014), 1061-1081. doi: 10.4171/JNCG/178