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arXiv · 1509.08318

Quasidiagonality of nuclear C*-algebras

Aaron Tikuisis·Stuart White·Wilhelm Winter
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Abstract

We prove that faithful traces on separable and nuclear C*-algebras in the UCT class are quasidiagonal. This has a number of consequences. Firstly, by results of many hands, the classification of unital, separable, simple and nuclear C*-algebras of finite nuclear dimension which satisfy the UCT is now complete. Secondly, our result links the finite to the general version of the Toms-Winter conjecture in the expected way and hence clarifies the relation between decomposition rank and nuclear dimension. Finally, we confirm the Rosenberg conjecture: discrete, amenable groups have quasidiagonal C*-algebras.

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Aaron Tikuisis, Stuart White, Wilhelm Winter. 2015-09-28. Quasidiagonality of nuclear C*-algebras. https://doi.org/10.4007/annals.2017.185.1.4

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