On the classification of simple amenable $\mathrm{C}^{}$-algebras with finite decomposition rank, II

We prove that every unital simple separable \mathrm{C}^{*} -algebra A with finite decomposition rank which satisfies the UCT has the property that A\otimes Q has generalized tracial rank at most one, where Q is the universal UHF-algebra. Consequently, A is classifiable in the sense of Elliott.

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Bibliographische Detailangaben
Veröffentlicht in:	Journal of noncommutative geometry Jg. 19; H. 1; S. 73 - 104
Hauptverfasser:	Elliott, George A., Gong, Guihua, Lin, Huaxin, Niu, Zhuang
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	14.06.2024
ISSN:	1661-6952, 1661-6960
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We prove that every unital simple separable \mathrm{C}^{*} -algebra A with finite decomposition rank which satisfies the UCT has the property that A\otimes Q has generalized tracial rank at most one, where Q is the universal UHF-algebra. Consequently, A is classifiable in the sense of Elliott.
ISSN:	1661-6952 1661-6960
DOI:	10.4171/jncg/560