Nuclear dimension and Z-stability

作者：Sato Yasuhiko; White Stuart; Winter Wilhelm^*

来源：Inventiones Mathematicae, 2015, 202(2): 893-921.

DOI：10.1007/s00222-015-0580-1

Simple, separable, unital, monotracial and nuclear C*-algebras are shown to have finite nuclear dimension whenever they absorb the Jiang-Su algebra Z tensorially. This completes the proof of the Toms-Winter conjecture in the unique trace case.
The structure theory of simple nuclear C*-algebras is currently undergoing revolutionary progress, driven by the discovery of regularity properties of various flavours: topological, functional analytic and algebraic. Despite the diverse nature of these regularity properties, they are all satisfied by those classes of C*-algebras which have been successfully classified by K-theoretic data, and they all fail spectacularly for the "exotic" algebras in [30,40] which provide counterexamples to Elliott's classification conjecture. The observation that there are deep connections between these disparate properties was crystallised in the following conjecture of Toms and the third named author.

• 出版日期2015-11