Quasidiagonality of nuclear C*-algebras

Aaron Tikuisis, Stuart White, Wilhelm Winter

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132 Citations (Scopus)
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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.
Original languageEnglish
Pages (from-to)229-284
Number of pages66
JournalAnnals of Mathematics
Issue number1
Publication statusPublished - 31 Jan 2017

Bibliographical note

Research partially supported by EPSRC (EP/N002377), NSERC (PDF, held by AT), by
an Alexander von Humboldt foundation fellowship (held by SW) and by the DFG (SFB 878).


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