Quasidiagonality of nuclear C*-algebras

Aaron Tikuisis, Stuart White, Wilhelm Winter

Research output: Contribution to journalArticle

55 Citations (Scopus)
4 Downloads (Pure)

Abstract

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
Volume185
Issue number1
DOIs
Publication statusPublished - 31 Jan 2017

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