Geodesic
Quasidiagonality of nuclear C$^{*}$-algebras
Aaron Tikuisis1 ; Stuart White2 ; Wilhelm Winter3
1 University of Aberdeen, Scotland
2 University of Glasgow, Glasgow, Scotland and Mathematisches Institut der WWU Münster, Münster, Germany
3 Mathematisches Institut der WWU Münster, Münster, Germany
Annals of mathematics, Tome 185 (2017) no. 1, pp. 229-284.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove that faithful traces on separable and nuclear $\mathrm{C}^*$-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 $\mathrm{C}^*$-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 $\mathrm{C}^*$-algebras.
DOI : 10.4007/annals.2017.185.1.4

Aaron Tikuisis 1 ; Stuart White 2 ; Wilhelm Winter 3

1 University of Aberdeen, Scotland
2 University of Glasgow, Glasgow, Scotland and Mathematisches Institut der WWU Münster, Münster, Germany
3 Mathematisches Institut der WWU Münster, Münster, Germany 
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Aaron Tikuisis; Stuart White; Wilhelm Winter. Quasidiagonality of nuclear C$^{*}$-algebras. Annals of mathematics, Tome 185 (2017) no. 1, pp. 229-284. doi : 10.4007/annals.2017.185.1.4. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.185.1.4/

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