Quasidiagonality of nuclear \(\mathrm{C}^\ast\)-algebras
type: Item
instance of: scholarly article
title: Quasidiagonality of nuclear \(\mathrm{C}^\ast\)-algebras
zbMATH Open document ID: 1367.46044
author: Aaron Tikuisis
author: Wilhelm Winter
author: Stuart White
published in: Annals of Mathematics. Second Series
publication date: 2017-02-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/1509.08318
review text: The main result of the paper is the following remarkable theorem: Let \(A\) be a separable nuclear \(C^*\)-algebra that satisfies the UCT. Then every faithful trace on \(A\) is quasidiagonal. This result has several important corollaries. Here are some of them: {\parindent=0.6cm \begin{itemize}\item[(1)] Every separable nuclear \(C^*\)-algebra with a faithful trace that satisfies the UCT is quasidiagonal. \item[(2)] The reduced group \(C^*\)-algebras of discrete amenable groups is quasidiagonal (this answers the Rosenberg conjecture). \item[(3)] Separable unital simple infinite-dimensional \(C^*\)-algebras of finite nuclear dimension that satisfy the UCT are classified by the Elliott invariant. \end{itemize}}
reviewed by: Vladimir M. Manuilov
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46L35
Mathematics Subject Classification ID: 46L80
Mathematics Subject Classification ID: 22D25
zbMATH DE Number: 6686586
zbMATH Keywords: quasidiagonal trace
zbMATH Keywords: quasidiagonal \(C^*\)-algebra
zbMATH Keywords: nuclear \(C^*\)-algebra
zbMATH Keywords: Rosenberg conjecture
MaRDI profile type: Publication
OpenAlex ID: W3098491911
arXiv ID: 1509.08318
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Quasidiagonality of nuclear \(\mathrm{C}^\ast\)-algebras (DOI)
DOI: 10.4007/ANNALS.2017.185.1.4