Classication of Simple C*-algebras — 1 articles found.

A Classification of Finite Simple Amenable Z-stable C*-algebras, II: C*-algebras with Rational Generalized Tracial Rank One

C. R. Math. Rep. Acad. Sci. Canada Vol. 42 (4) 2020, pp. 451-539
Vol.42 (4) 2020
Guihua Gong; Huaxin Lin; Zhuang Niu Details
(Received: 2020-09-20 , Revised: 2021-01-31 )
(Received: 2020-09-20 , Revised: 2021-01-31 )

Guihua Gong, Department of Mathematics, Hebei Normal University, Shijiazhuang, Hebei 050016, China
and Department of Mathematics, University of Puerto Rico, Rio Piedras, PR 00936, USA; e-mail: ghgong@gmail.com

Huaxin Lin, Department of Mathematics, East China Normal University, Shanghai 200062, China and
(Current) Department of Mathematics, University of Oregon, Eugene, Oregon, 97402, USA; e-mail: hlin@uoregon.edu

Zhuang Niu, Department of Mathematics, University of Wyoming, Laramie, WY, USA, 82071; e-mail: zniu@uwyo.edu,

Abstract/Résumé:

A classification theorem is obtained for a class of unital simple separable amenable \({\cal Z}\)-stable C*-algebras which exhausts all possible values of the Elliott invariant for unital stably finite simple separable amenable \({\cal Z}\)-stable C*-algebras. Moreover, it contains all unital simple separable amenable C*-algebras which satisfy the UCT and have finite rational tracial rank.

Dans cet article et le précédent on donne une classification complète, au moyen de l’invariant d’Elliott, d’une sous-classe de la classe des C*-algèbres simples, moyennables, séparables, à élément unité, absorbant l’algèbre de Jiang-Su, et satisfaisant au UCT, qui épuise l’ensemble des valeurs possibles de l’invariant pour cette class. La partie I réalise une grande partie de ce projet, et la partie II l’achève.

Keywords: Classication of Simple C*-algebras

AMS Subject Classification: General theory of $C^*$-algebras, Classifications of $C^*$-algebras; factors, K-theory and operator algebras -including cyclic theory 46L05, 46L35, 46L80

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