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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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The Jiang–Su algebra revisited

Mikael Rørdam1 / Wilhelm Winter2

1Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark. e-mail:

2School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom. e-mail:

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2010, Issue 642, Pages 129–155, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crelle.2010.039, February 2010

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We give a number of new characterizations of the Jiang–Su algebra 𝒵, both intrinsic and extrinsic, in terms of C*-algebraic, dynamical, topological and K-theoretic conditions. Along the way we study divisibility properties of C*-algebras, we give a precise characterization of those unital C*-algebras of stable rank one that admit a unital embedding of the dimension-drop C*-algebra Z n, n+1, and we prove a cancellation theorem for the Cuntz semigroup of C*-algebras of stable rank one.

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